Back in '10 I got my shoebox shipped from Miami to SF and it cost me 1k. Besides the bill's impact on my wallet, it was painless. Go to the a1autotransport.com website (company I used) to learn more. The only advice I'd leave is know a quote is not a contract. Your quoted price may be different from your terminal pick-up price.
I shipped my car from Orange County to RI. It took about 2 weeks and cost $950. I had my Mazda dealer handle everything. The car came in one piece with some minor cosmetic issues. There was a scratch on the rear bumper and the front bumper scraped going on/coming off the truck.
Seeing as how this thread was from 10 years ago, I hope the OP had a better experience!