Whenever you hand your goods (including your car) to a second party, you should first check what coverage you are offered in case of damages.
Motor carriers are required by the FMCSA to hold both liability and cargo insurance. Auto transport brokers do not need cargo insurance, since they do not own any trucks and do not directly handle the transport. Nonetheless, a respectable auto transport broker will require proof of insurance from the carriers they hire.
What does all this mean to me?
It means that you are covered in the unlikely event that your car suffers any damages. In the event you work directly with a carrier, it is still wise to inquire about the exact terms of the insurance (e.g., type of damages covered, the limit of their insurance, deductibles etc.).
Don’t forget to check with your own auto insurance agent to learn about their policies regarding car shipping.