How does one determine the value of rare, classic cars?

There are a few cars that I am interested in buying at some stage, that are incredibly rare, and currently I cannot find any for sale. When the time comes, I may have to directly approach an owner, as they are unlikely to even be advertised. But how do I work out what a fair price is? For regular cars, there is a market to compare price with, and websites that list average kilometres and price for that particular vehicle. When it is something rare though, there is not a large enough sample of recent sales to be a reliable gauge. What should I be prepared to pay? How would an insurance company determine an agreed value?