Always ship convertibles with the top secured properly. Seal any holes or open seams in the top to prevent moisture damage. If you cannot raise the top, consider closed container shipping.
Have a charged and relatively new battery, properly inflated tires, and make sure all fluids are at adequate levels. If you have ANY leaks from your car, be sure to tell transporter so that he will position you car properly. Cars leaking oil and especially brake or transmission fluid should NEVER be on the top of a two deck open trailer. This is to prevent leaks onto the paint of vehicles below. More information on moving vans for rent here.
You should keep a photocopy of your registration and insurance paperwork for the vehicle in the glove compartment.
Prepare a careful list of any operational problems or steps necessary to start, stop, or drive your vehicle on or off the trailer.