I've had 2 vehicles shipped; one from Iowa to Virginia, the other from Oklahoma to Virginia.
You need to do some planning before you call anybody for quotes, such as: Do you want it shipped enclosed, or on an open trailer; at both departure and arrival points, is there access for an 18 wheeler, either literally right at your door, or maybe down the street; do you want door to door service, or would you be willing to take the car to a terminal for shipping, and pick it up at a terminal on the other end? Do you want the car covered, or separated from others perhaps on top of it, to ensure no fluids could leak down onto your paint? Once you make those decisions, you've already narrowed down the field a bit. From there, go to hemmings.com, and look under transport. The one thing you really want is an owner-operator which is fully insured and bonded, and does very detailed inspection reports on both ends. You do NOT want someone that brokers the deal for you, as that's setting up an insurance nightmare if anything goes wrong.
As for cost, it's a bit more than a couple hundred dollars. For a top-flight shipper, enclosed, door to door, at that distance, I'd guesstimate you're looking at $800-$900, maybe a bit more. But, for the money, comes peace of mind.
I used these folks:
http://www.dasautoshippers.com/
If you want nothing but the best, this is the one:
http://www.intercitylines.com/
Jerry