Collector car insurance and airplane insurance is typically written on an "agreed value" basis, where the insurer agrees at policy issuance that the car/airplane is worth $X if declared a total loss. We had a collector car insured through Hagerty that was hit by a red-light runner. They were amazing to deal with and paid the agreed value (minus the value of the crashed chassis that we bought back from them) within just a few days and went after the at-fault driver's insurance without us having to hassle with anything.

Airplanes and collector cars do not have a readily available source of "comps" to determine value and in both cases, the cost to recreate a given condition is typically higher than the value of that car/airplane in the open market. I can have an airplane that is "worth" $250K to me, that I could only sell for $200K, but that would cost $300K or more to recreate exactly by starting with an available airplane and re-customizing the avionics and airframe mods exactly. In such a case, I can probably get a policy written for any agreed value as low as I want (at the risk that I'd get cut a check for that amount and have no airplane in the event of a loss) and pretty close to $300K.