As of my knowledge cutoff in September 2021, one of the most expensive samurai swords ever sold at auction is the Fudo Myo-o Katana. The Fudo Myo-o Katana is a 14th-century Japanese sword that fetched a price of 1.2 million euros (approximately 1.4 million US dollars) at an auction in 2016.

The Fudo Myo-o Katana is renowned for its exceptional craftsmanship, historical significance, and artistic beauty. It is attributed to the renowned swordsmith Soshu Yasutsugu, who was active during the Nanbokucho period (14th century). The sword is adorned with intricate engravings, gold inlay work, and a hilt wrapped in sharkskin and adorned with a menuki (decorative grip ornament).

It's important to note that the value of samurai swords can vary significantly based on factors such as the swordsmith, historical importance, condition, age, provenance, and the demand among collectors. While the Fudo Myo-o Katana is an example of an exceptionally expensive samurai sword, there may be other swords with equally high or even higher prices that have been sold privately or are held in private collections.