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I found a challenge coin display that works well for this, as you can see. I believe that there are quasi-standard sizes.
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Oh, that's nice! I've got to find me one of those!
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This is the precise product from the picture, which the coin fits into perfectly (it's the 2" clear variant): amazon.com/gp/product/B00
It works best if you put it on a shelf at about eye level. Something like that. It's not really suitable for displaying the coin on a coffee table, since it must stand upright.