I would use needle nose pliers to remove it from any chains if you want and tack it up with straight pins!
You could use metal glue or all purpose glue.
I think that you can attach jewelry to the back or bottom of a shadow box using E6000 glue, but a lot depends on how permanent you want the shadow box to be. You could cut Styrofoam to fit the box and wrap it in fabric and then use pins or staples to get the jewelry to stay where you want it. That would be more temporary, leaving you the option to remove the jewelry or change it out.
Here are some hometalk ideas that might help:
Pins, hot glue, stick pins.
You could cover foam board with fabric (gluing it to the back of the foam board), and then find areas on the jewelry where you could stitch it to the fabric. Another option for necklaces with chains is to use a piece of luan cut to size for your back. Then you could stain, paint, or again cover it with fabric. To hang the necklaces you would use the smallest cup or decorative hooks that you can find that will fit inside the shadow box and screw them into the luan. Then you can hang your necklaces from the hooks. If you do an open front shadow box, your necklaces are still accessible if you wanted to wear them or change the display).
You could also use the smallest screw eyes that you can find, screwing them into the luan. Put 2 of them level with each other and far enough apart that you could put the pin part of a brooch through the 2 eyes and be able to close the brooch.
A thin piece of cardboard either painted or printed paper glued on in the back of your shadowbox. Poke some tiny holes in it where you want your jewelry to be. Take a piece of sewing thread & with a needle threader, insert the end of the thread thru the hole. Wrap it around the end of the piece of jewelry & re-insert it back into the hole it came out of. Pull it snug & it will keep the jewelry in place. On the back, place a piece of tape to secure the thread. Repeat for other jewelry. If you're using pictures like in the one above, adhere some picture corners to your paper & just insert your picture. You can interchange the pictures from time to time if you like using this method OR make more shadowboxes lol. Once done with your set-up. Just insert the piece of cardboard into the box, no adhesive required if it's cut the exact same size as your box & fits snugly in. Hope this helps. :)
Thanks so much for this info. I’ve collected brooches I want to display. Thought they would have to be glued on somehow!