As Andy said use Intercity Lines. They are fast, reliable and even have a $150 option not to move the car during hte trip. Ive had my car transported several times, and they are one of the best. Ive also used Exotic Car Transport, and they service Florida. Nice trucks, and a slick operation as well. I think they are a bit pricier.
Andy posted the url and contact infor for intercity. You may also want to check out exoticcartransport.com. They may have the best service between cali and florida (since they are florida based). I know symbolic motorcars in la jolla/san diego uses them pretty exclusively for this route.