Price of Tudor-era Jewelry

I don't know prices of jewellery but you do need to pin down the following before you go much further.

Which part of the Tudor era?
How well preserved?
How large?
What quality of stone and workmanship?
What provenance?
Which metal?

Try going to auction house websites and searching past sales.

I also don't think that many historical societies buy high ticket items - or indeed any items. The ones I've run into are all about discussing information and having meetings in chilly church halls.

Forget about selling it to a historical society; they'd take it as a donation, but they don't pay out for much of anything. The auction house would be more likely to take it on consignment to sell, rather than buy it.

Are you trying to sell this in the real world, or is this in a work of fiction?

I'd assumed it was for fiction - good point King N.

Continuing to assume it is for a work of fiction, what the OP might want to do is to trawl through auction house catalogues and find something of the right period and price and describe that in the book, rather than first inventing the look of the jewellery and trying to find out its price. Unless of course the appearance is already key to the story.
Just a thought on speeding up the research. I'm keen on good research, but it can be time consuming, so ways of minimising research can be useful.