On car arriving to its destination, inspect the outside of the car to ensure that it is not damaged. If you find damage to the body of the car, file a claim immediately.
And by taking the proper precautions, such as buying auto shipping insurance and inspecting your car before the trip, you will be able to ensure that your car will be safe during transportation.
Prior to resolving on which auto shipping company to use, inquire the shipping companies you are paying attention in for their insurance certificate, as all the companies should have one. Find out whether your car will be enclosed for any damage, which happens during shipping, or whether there are only some parts of the car (i.e. the body) covered. Also check whether you are obligatory to pay a deductible.
Get any promises or declarations from the auto transport company in writing.
In case you see any damage done to your vehicle during the shipping process, note it on the bill of lading, get the driver to sign it and then get in touch with the auto shipping company directly for reimbursement.
Of course, it might be a lot to procedure, but it is the only way to make sure your auto transport insurance is set up right.