As of my knowledge cutoff in September 2021, one of the world's most expensive swords is the Honjo Masamune. The Honjo Masamune is a legendary Japanese sword forged by the renowned swordsmith Goro Nyudo Masamune during the 13th century. It is considered a national treasure in Japan and is known for its exceptional craftsmanship and historical significance.

The Honjo Masamune was once owned by several prominent figures in Japanese history, including the warlord Toyotomi Hideyoshi and the Tokugawa shogunate. However, its current whereabouts are unknown, and it is believed to have been lost or destroyed.

While the exact value of the Honjo Masamune is difficult to determine, it is widely considered to be an invaluable cultural artifact. Some estimates suggest that, if it were to appear on the market, it could potentially fetch a price in the range of tens of millions of dollars.

It's worth noting that the market for antique swords can be highly specialized, and the value of a sword can be influenced by factors such as its historical significance, rarity, condition, provenance, and the demand among collectors and enthusiasts.