I think a lot of the tintypes were given out with only a matte on them. The corners were clipped and the brass matte bent over at the four corners.
Paper mattes were used too. I use one for my quarter plates that was copied from an original by Will Dunniway. It consists of a matte with a tombstone shaped opening that goes into a paper folder. It has 2 gold lines around the tombstone window.
I see a lot of CW period gem sized and larger tintypes in paper CDV sized mattes.
Here is a page I found on the net. I didnt read it all for accuracy but it looks pretty good.
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freepages.genealogy.rootsweb.com]