You can get special insurance, and really it's not all that costly. However, there are car age, mileage driven, and garage requirements that usually are not the easiest to fulfill. Some companies ease up on one requirement like age, so you can insure a newer car, but then you can barely drive it and it must be indoors all the time and vice versa.
A friend of mine has speciality insurance on his '95 Trans Am Comp T/A, and the restrictions are strict on what he can do with the car. If he drives it too much or does something the company doesn't like, NO coverage. Kinda scary to me.