The cost of a genuine, authentic Japanese katana can vary significantly depending on various factors such as age, condition, quality, and historical significance. As highly sought-after collector's items and works of art, authentic Japanese katana can be quite expensive.

Antique or historical katana, which were crafted by master swordsmiths and hold historical value, can be extremely costly. These rare and well-preserved swords can command prices ranging from tens of thousands to several hundreds of thousands of dollars or even more, depending on their provenance and quality.

Contemporary Japanese swordsmiths also create handmade, authentic katana using traditional techniques. These modern katana, known as "shinsakuto," can be purchased from reputable swordsmiths and dealers. The price of a newly crafted, authentic katana can vary widely based on the reputation of the swordsmith, the materials used, and the craftsmanship involved. Generally, they can range from a few thousand dollars to tens of thousands of dollars.

It's important to note that due to the value, historical significance, and regulations surrounding Japanese swords, it is advisable to consult with reputable dealers, experts, or swordsmiths who specialize in Japanese swords. They can provide accurate information, guidance, and help ensure the authenticity and legality of the katana being considered for purchase.