What Dave said is basically it. My brother in law is an insurance adjuster and basically explained to me that if your expensive collectibles were damaged or stolen they're just going to see "Star Wars Action Figure" and pay you what a Star Wars Action figure costs. Doesn't matter if it was vintage Yak Face or 1995 Leia. I got the impression that this would mean whatever the current retail price is, so I don't know if they'd see your vintage figures as being based on 1980 prices or 2016 prices. I sort of remember concluding that if a figure costs $8 to $13 right now, I'd be happy enough with that kind of payout if things went to hell and didn't worry about it as much.
There are other companies that I have heard are reputable that specialize in insuring collectibles only.
I THINK this is the one they were discussing at Rebelscum the last time this came up that I noticed:http://collectinsure.com/
But I'd have to go through and double check somehow. I started trying to come up with a number for my collection to get it insured separately but it's fallen to the back burner lately. Between Hasbro, Lego and Gentle Giant, I'm terrified of what the number actually is, and worried that I'm really under insured on that stuff. This might be the reminder I need to get back into that research.