How do we value our cars?

I don't think the insurance company cares about real value if there is truly such a thing. They will go with book value or the agreed value if you have one, the 57 Chev was a perfect example. Appraisals always seem over the top high so I doubt that would help much. I don't know anything about your car but 16 - 20K seems pretty high if you were trying to sell it in these times.

It's worth what you can get for it, so finding similar cars sold would go a long way