It would take a bit and it's an iffy project, but you could mold one out of plastic, or plexi-glass. It'd be seen, but you can only do so much if you want a sheathe. Otherwise, there are always ways of mounting a katana on your back, like o01101011 said, the clear bra strap material, or fishing line, though I don't personally recommend either, as the fishing line can cut in, even with the costume on.
You could, however, try to incorporate something like the clear bra strap material into the back of your costume that the katana can easily slide in and out of without being directly noticeable.
Kirito (Aincrad, not ALO)
Ino Yamanaka 75% (Need wig cut and styled)
Pink Power Ranger (possibility)