After my recent experience, I would suggest finding (if you can) a shipper without going through a broker. All a broker does is put out the job on a board for bidding, then takes 15-20% for not much work. In my case, I had exactly one bidder, and the company wasn't the most professional. The shipping company was located near Seattle. My contract was to deliver the wagon to Portland. It was trucked from Wisconsin to Seattle, then some company flunky drove it to Portland (in bad weather, I might add...).
I've had a bunch of cars shipped and if the car is nice the only way to go is with an enclosed transport and with a big outfit like Reliable or Intercity. If you're looking for cheap you can use brokers and one horse outfits but they can turn into real horror stories and more often than not do. I've never not had problems with them and I've used the top recommended and rated outfits. They're only as good as the worst drivers that bid on their jobs and I almost always get them. But some cars aren't worth the fancy transport so you just have roll the dice and hope for the best.
I went online the first time to a site that you can go to that gives reviews on carriers and rates them...one star, two stars, etc. It really didn't do much good to do all that. BlueVista probably said it the best. Do some research and check reviews and roll the dice. Do NOT use the carrier that eBay uses...I think it's called DNS or something like that. Most every car forum online has this thread and there seems to be no operative answer. Good luck, jmt.