A buddy of mine has his 65 Malibu Convertible insured with
http://www.hagerty.com . I think they only do classic cars and boats. I wanted to do it for one of my cars and looked throught the site to check it out. They ask about your usage of the vehicle. I believe you are only supposed to drive it a certain amount of miles per year. You also might need antique/classic plates.
Also the car should be basically stock. There are also other rules that are not unreasonable if it is a classic that doesn't a ton of road time and it is cheaper than regular insurance. I believe lots of regular car insurance companies are offering a from of classic car insurance as well.