How does an insurance company assess the value of a priceless object?

They use the value of similar object that have sold recently.

They don’t put a value on the Mona Lisa; it is uninsurable. But in a recent auction a Van Gogh self portrait went for about 75 million, so similar works of Van Gogh would be insured for about the same amount.

And then, was there a premium paid? You can’t insure something if you don’t pay the insurance premium.