Darth Sidious' lightsabers
The lightsabers of Palpatine were a pair of Sith lightsabers forged by Palpatine, otherwise referred to as Darth Sidious, the Dark Lord of the Sith.
Specifications

As a connoisseur of fine arts, Darth Sidious imbued his initial weapon with exceptional artistry, evidently reflecting the Sith Lord's fondness for ancient aesthetics. The lightsaber's hilt was constructed from nearly impervious phrik alloy, while the flat emitter was crafted using aurodium. The entire weapon boasted a sophisticated and elegant electrum finish. A synth-crystal was used as the weapon's focusing crystal.
Being a practical individual, Sidious had already created a secondary lightsaber. This weapon mirrored his primary lightsaber in its initial design, featuring the same electrum and phrik finish, but it was later modified with an unidentified black alloy.
In reality, Sith individuals typically possessed sufficient powers to engage in combat without lightsabers. However, every apprentice was still taught how to wield one as part of their training. Sidious himself believed that he and his contemporaries had transcended the need for lightsabers, and only continued to carry them as a means of mocking the Jedi. He ultimately regarded his own lightsabers as mere affectations, seldom employing them in actual combat.
History
Creation and early usage

During his apprenticeship, Darth Sidious fashioned his initial lightsaber, which he utilized throughout his Sith training under Darth Plagueis. Upon embarking on his political career, he concealed this lightsaber within a neuranium statue of Sistros, commissioning the piece to be built around his weapon. The lightsaber remained hidden within the statue for a minimum of two decades, awaiting Palpatine's eventual need for it. During this time, the Sith Lord was compelled to employ backup weapons whenever he needed to wield a lightsaber. On one occasion, he was even required to use his Master's lightsaber in conjunction with his own. At another point, he generated a second lightsaber as a backup weapon.
Clone Wars
In 20 BBY, Darth Sidious made use of his lightsabers on a couple of occasions during the Clone Wars.
Mandalore
Upon discovering that his former apprentice Darth Maul had survived a twelve-year exile and was present on Mandalore with his brother Savage Opress, having conquered the planet, Sidious brought his two lightsabers and journeyed to the Sundari Royal Palace aboard his personal shuttle, where he confronted the two Zabrak brothers. After exchanging a few words with Maul, he brandished and engaged both lightsabers to battle the pair. His movements during the duel were erratic yet fluid, even going as far as to damage the palace floor.
Sidious proved to be too formidable for them. While he was unable to swiftly defeat the brothers, he ultimately managed to separate them. After Opress recovered from a kick delivered by Sidious, Sidious initially evaded Opress's attacks effortlessly without activating his lightsaber before igniting his lightsabers and engaging Maul's brother. He proceeded to completely overpower Opress and swiftly impaled the Nightbrother with his lightsabers, resulting in his death. Sidious, after another brief exchange, descended with both lightsabers and resumed dueling Maul with immense ferocity. Despite Maul's significantly more intense resistance, Sidious ultimately disarmed the Zabrak Sith Lord and then sheathed his lightsabers within the folds of his robes, having emerged victorious from the duel and incapacitating Maul.
Korriban
On Coruscant, Darth Sidious plotted to assault Jedi Master Yoda (who was then on Korriban) utilizing Sith sorcery; he exploited his second apprentice Darth Tyranus's connection to the elderly Jedi Master to achieve this. Employing a drop of Tyranus's blood, Sidious conjured an illusion fueled by Force lightning depicting both Sith Lords. After failing to deceive Yoda with an illusion of Sifo-Dyas, Sidious generated a second illusion in which Yoda was aboard a Republic gunship en route to The Works district of Coruscant. Following Anakin Skywalker's engagement with Tyranus in a lightsaber duel that resulted in the elderly Sith apprentice's defeat (foreshadowing his actual demise at Skywalker's hands), Yoda and Sidious dueled on an outdoor walkway, each wielding a lightsaber. Although Sidious fought Yoda evenly, he employed Force lightning to incapacitate Anakin. Sidious persisted in battling Yoda as the situation deteriorated when Anakin's unconscious body began to plummet from the walkway destroyed by Sidious. Despite Sidious's taunting use of Dun Moch, Yoda employed the Force to prevent the young Jedi Knight from falling (despite being an eventual threat), willing to sacrifice everything, including himself, in order to save his friend. Yoda and Sidious fell to the ground below and the former found himself holding nothing but the Sith Lord's empty robes. His final trial complete, Yoda awoke from his nightmarish vision and returned to Coruscant.
The Galactic Empire's rise
Showdown on Coruscant

In 19 BBY, Palpatine revealed to Jedi Knight Anakin Skywalker that he was a Sith Lord. As Mace Windu and his Jedi companions hastened to the Senate Office Building to confront him, Palpatine preemptively retrieved his lightsaber to ensure he was armed upon their arrival. He retrieved it telekinetically by igniting it within the statue and seizing it once it burned its way out. Concealing the weapon within his sleeve, Palpatine awaited the Jedi. Following a brief exchange intended for an audio recording device hidden within his office, the Supreme Chancellor brandished the weapon. With a battle cry, the Sith Lord lunged at the Jedi, swiftly eliminating Agen Kolar and Saesee Tiin. After killing Nautolan Kit Fisto, the duel was solely between Palpatine and Windu.
Initially gaining the upper hand, Palpatine pressed his advantage against Windu. However, Windu's Vaapad technique enabled him to counter the Sith Lord's rage-fueled assault. The Jedi directed the battle toward the bay window of Palpatine's office and onto the windswept ledge outside. The perilous position of the battle prompted Palpatine to divert some of his power into a Force-grip on the permacrete, slightly diminishing his speed. Windu swiftly disarmed the Sith Lord with a precise kick to the face, disrupting Palpatine's balance and causing him to drop his lightsaber as he struggled to maintain his footing. The lightsaber plummeted from the window into the bottomless streets and alleyways of Coruscant below just before Skywalker arrived. Consequently, it also forced him to rely on a single lightsaber.
Showdown within the Senate

Similar to his initial weapon, Palpatine concealed this lightsaber within his sleeve. When the Jedi Grand Master Yoda confronted him after Order 66, Palpatine brandished the weapon. During their lightsaber duel, they appeared evenly matched until Yoda knocked Sidious's lightsaber from his grasp. Overwhelmed, the Galactic Emperor telekinetically assaulted Yoda. Leaping onto one of the delegation pods within the Senate arena, Palpatine attempted to overwhelm the Jedi Master by hurling numerous pods using the Force. Ultimately, the fierce duel concluded when Yoda countered Sidious's telekinetic assault and forced him into close range, prompting the Sith Lord to employ Force Lightning to disarm Yoda of his lightsaber, only for Yoda to ultimately redirect it back after a tremendous struggle. The resulting blast separated Sidious from Yoda, and the diminutive master chose to retreat.
Later uses
When his third apprentice Darth Vader set about crafting his own lightsaber, Palpatine offered his elegant weapon as a model, as well as the synth-crystal that powered Vader's weapon. Vader regarded Palpatine's lightsaber as little more than an antique, and while respectful of its high level of craftsmanship, he preferred a weapon with more ballast. Vader's resulting weapon was little more than an enlarged version of his first Jedi lightsaber, machined out of a black alloy.
Palpatine carried the lightsaber for a significant portion of his life afterward, though he rarely wielded it in combat. His position as Emperor resulted in infrequent encounters with other Force-users, and he generally preferred to rely on his innate abilities with the Force. Notably, he did brandish his lightsaber during the rebellion of the Sa Cuis clones, though he never actually used it, as Vader dealt with the uprising himself.
Stolen

When Galen Marek confronted him and Darth Vader in 2 BBY with the intention of rescuing the recently captured Rebel leaders, Palpatine remained passive and allowed Vader to engage the Force-adept. After Marek defeated the cyborg, Palpatine attempted to persuade him to slay Vader and assume his position as apprentice. As Marek pondered the proposition, captured Jedi and Rebel leader Rahm Kota took action. Telekinetically seizing Palpatine's lightsaber, Kota eliminated the guards holding him and lunged at Palpatine.
Palpatine incapacitated Kota with a blast of Force lightning. However, Kota's actions spurred Marek to attack the Emperor rather than Vader, during which Palpatine fought his assailant with both the Force and his recently recovered lightsaber. This weapon would survive into the Legacy era and was an object the One Sith wished to claim.
Replacement

By 10 ABY, Sidious maintained a collection of stolen Jedi lightsabers within his laboratory on the Imperial throne-world of Byss for potential use, one of which emitted a blue blade. Following Luke Skywalker's destruction of numerous Sidious clones, Sidious's essence transferred into one of the surviving clones. The newly possessed clone then seized his blue-bladed lightsaber from the lab wall and employed it to duel Luke. He emerged victorious in the duel, successfully persuading Luke to embrace the dark side and become his apprentice.
Later in 10 ABY, aboard his Super Star Destroyer Eclipse, he discovered that Luke Skywalker had rejected the dark side due to the efforts of his twin sister, Leia Organa Solo. Enraged, Sidious wielded his blue-bladed lightsaber to attack Luke. Despite the Sith Lord's formidable power, Skywalker caught him off guard. Moments later, the Eclipse was destroyed, along with Sidious's clone.