It may vary state to state, but State Farm has insured my car since 2005 for an agreed value ($35k?). There are no limitations on use, other than mileage upon which the rate is based. I had to get a professional appraisal, but that was pretty easy.
I had done no business with State Farm before this, and switched to them specifically for the coverage. They wanted at least one other piece of "normal" business in order to write the policy, and they now have 3 houses (mine and two rentals), two cars, the speedster, and a VW bus. They were great on a hail damage claim for one of the houses and the minivan, but I have no idea if they'd balk with a claim on one of the classics. It's not as cheap as Grundy or Hagerty-- but it is very reasonable for the peace of mind I've got.
I had Hagerty and American Modern (before State Farm) on the two speedsters I had before this one. Hagerty paid a claim for a bad paint scrape I got pulling into the garage a bit too close to a pancake air compressor. It's been 16 years, but they let me go where I wanted and paid the whole thing without deductible.
I would have stayed with them, but the limitations on use spooked me. I read the actual language of the policy and became concerned that in a real claim situation (where the car is the least of my concerns-- personal injury liability is what scares me), they could point to the "show and parade" clause and deny coverage.
Everybody judges insurance by how they do in a minor claim (like, up to $50k)-- I'm much more concerned with how they might handle something where I kill or main myself, a passenger, or somebody else. That's the reason insurance came into existence-- not to pay for a paint scratch, and that's what I'd be shopping for, personally.
Your mileage may vary.