Generally speaking high performance or sports cars command a premium when it comes to insurance. Generally these cars are considered more likely to be involved in an accident, although statistically less likely to be stolen than your Vauxhall Astra or Ford Sierra.
Many providers specialise in sports car insurance but beware some may insist you install a tracking device before they will insure you.
Many sports car makers offer their own insurance for their own cars, generally you can get a better deal if you are prepared to shop around but for some people the car manufacturers insurance scheme may be satisfactorary.
Generally the older your age the cheaper your insurance on sports cars will become. The theory being that older people are more sensible than boy racers. Sometimes true but often not!
The insurance group for sports cars generally is higher than that of your family saloon, this also helps increase your premium. As does the soft top conventially associated with high performance sports cars.
Generally for sports enthusiasts the insurance premium is something they live with and would never put them off buying their dream car.