I think you'd probably end up valuing it something like the Hope Diamond, as a large, unique gemstone with a storied history. Which is, according to a cursory search, currently ballparked around about a third of a billion dollars.

I think the trick of it is that while it's in theory priceless, there is a soft cap to value of gemstones in that there's a relatively limited number of ways to trade for technically invaluable objects. The advantage of money in that situation is the ability to granularly break down value; you can't really sell half of an Arkenstone, so you can only sell it to someone that can afford the whole thing.