Since it was #266/300 and extremely low mileage, I attested that it was worth significantly more than KBB. My insurance carrier was willing to write me a policy for more coverage than KBB, with a few stipulations. I was basically limited to 3k miles/year, and I also had to pay more for the coverage, but I felt it was worth it. A Nissan dealership in Kansas City wrote me a letter stating that the car would fetch well beyond KBB because of its rarity, and that was sufficient for my carrier. My coverage has gone down over time because it is also subject to depreciation, but it is still well above KBB (which is only $13.9K on a '96TT with 9K miles). I think you should just ask several different insurance companies- many will have some excess coverage option, but you will have to pay for it...
Anyone who thinks mycar is only worth $13K is insane...
