Most transport companies are brokers who work with many independent contractors. One that comes straight from the PCA E-brake newsletter:
American Auto Transporters, Inc., which is supposedly owned by a PCA member. Another place to get a quote might be
Intercity Lines, Inc., who sponsors the Rennlist forums and has good reviews. I have used Plycar myself, and found them to offer very professional service in an enclosed, lift-gate transporter:
http://www.plycargroup.com/I have seen others recommend Reliable and Horseless Carriage as well. Depending on your schedule and location of the car and destination, prices can vary.
Good luck,
TT