I just recently had my car moved to a restoration shop for the body restoration. I started by searching for the shop that I wanted to do the work. IMO, this is the most important step - way more important than what it will cost. Look at lots of cars done by the shop to get a feel for their quality level and how consistent their work is. I was lucky since the shop I chose turned out to be less than 10 miles from my house, and it turns out the owner lives about 1/8 mile from me. Small world. Anyhow, I met with the shop and showed them a bunch of pictures. They gave me a very broad estimate from the pictures and my description of the car. They then wanted to set up an inspection of the car to refine their estimate. I was definitely more worried about the quality of the work than getting an accurate estimate, so we skipped this step. To me, the car is what it is and needs whatever work it needs to be done right. So, we made our agreement, and they came & got the car with their equipment.
I would think that any good shop would be willing to come see the car in order to provide you with an estimate. They should also be able to transport the car to & from their shop. As previosly mentioned, none of this is free and I assume that they would bill out at their normal hourly rate (or perhaps slightly less) for these services.
Also, make sure that your car is insured, even though it may not be registered or driveable. Make sure that the insurance covers trailering and loading/unloading. I was able to get insurance that covered all this through Hagerty.