Determining the most valuable sword is subjective and can vary depending on several factors such as historical significance, craftsmanship, rarity, provenance, and cultural importance. Here are a few swords that are often considered among the most valuable:

1. Honjo Masamune: The Honjo Masamune is a legendary Japanese sword made by the renowned swordsmith Goro Nyudo Masamune during the 13th century. It is considered one of the finest examples of Masamune's work. The sword is designated as a national treasure of Japan and is highly revered. The current location and ownership of the Honjo Masamune are unknown, adding to its mystique and value.
2. Joyeuse: Joyeuse is the legendary sword associated with Charlemagne, the medieval King of the Franks and the first Emperor of the Carolingian Empire. While the original Joyeuse is lost to history, various swords claim to be replicas or inheritors of its legacy. The historical and cultural significance of Joyeuse contribute to its perceived value.
3. Napoleon Bonaparte's Sword: Napoleon Bonaparte, the French military and political leader, had several swords during his lifetime. One of the most famous is the sword he carried during the Battle of Marengo. Napoleon's swords, especially those associated with significant events or battles, have been highly sought after by collectors and have fetched substantial prices at auctions.
4. Wallace Sword: The Wallace Sword is a medieval Scottish sword associated with Sir William Wallace, a national hero of Scotland. The sword, currently on display at the National Wallace Monument in Scotland, is considered an important historical artifact and symbol of Scottish resistance. While its monetary value is difficult to ascertain, its historical and cultural significance make it highly valuable.

These are just a few examples, and the value of a sword can vary based on historical importance, provenance, condition, and desirability among collectors. Swords with strong historical connections, ties to renowned figures, or those embodying cultural and national significance tend to be highly prized and command high prices when they appear on the market.