Car insurance is typically more expensive for a convertible than a car with an attached top. The exact price difference will depend on the insurance company.
Insurance companies will also use other factors to determine the price such as age and marital status of the driver. Previous driving records will also be taken into consideration. Typically, a person with a convertible with a hard top will pay less for insurance than a person with a convertible containing a soft top. Car insurance companies typically believe that convertibles are easier to break in to and that if the car is wrecked, it will suffer more damage.