You found two so far, so let's get a little optimistic.
You can buy ring display boxes but the nice kind with an attached glass lift up lid can be pricey.
I have this one I won at a club hunt as a prize, cheaper to buy with just a lift off lid.
These are just a few of my rings from years ago but a lot of that gold is sold, now, I replaced the cheap ones on the bottom row with nicer ones as I found them and I have added a lot more to my collection since then that should fill up another case or two.
These aren't even most of my real junky rings, all of those go into a pickle jar.
Pretty inexpensive on Ebay, this one is under $10...
https://www.ebay.com/itm/100-Slot-J...a375afc4048749681b4acad860e8a&redirect=mobile
They are even cheaper if you get them from Ali Express.
Gotta wait a bit to get them from that Chinese company but it gives you more time to find more rings.
You can go to the dollar store or Goodwill and buy a cheap little box, throw a little foam and fabric in there and cut some slits like this one I made for the best display contest we had at my club for one month of finds.
I had found 3 gold, (the one with the natural pearl was 24k), and two honking silver rings in the last three weeks before this meeting so I wanted to make a good impression to win the contest.
Box was $2.99 from Goodwill, about $3 for the foam and fabric from a craft store...I had the razor blade to cut the slits.
Or...you can just make one up yourself with no box.
JoAnne fabrics and crafts, Michaels or any other craft store should have what you need.
A cheap foam block, a small piece of dark fabric draped over it and glued down underneath, a razor blade to cut a few spots in the top and viola, a fine way to display these two and many future rings.
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A jar is okay but if you buy or build your own in such a nice way to display them like this you can admire them anytime you like with just a glance and all the extra empty holes will motivate you to get out there and find more.
It works...trust me.