This photo shows the first swap items I ever made, a pair of tags for a summertime swap. The left tag has a sun that I handmade from wire using a jig and a shadow box with a real dried starfish in it.
The tag on the right features a dimensional butterfly made with an Accucut die. The diecut has perforations down each side of the body so you can bend the wings up. I stacked two and glued them down the middle and added wire antennas.
The scrapbook shop that had this particular Accucut die shut down last year, but I still make the dimensional butterflies using Martha Stewart's butterfly punches. I just use a scoring tool to make a slightly curved score line down each side of the body then assemble them the same way, with glue down the middle. They are super cute! If they are in a position to be smashed (like in a scrapbook) I sometimes add a small piece of foam dimensional under each wing to keep them permanently popped up. This same technique works great for flower petals, too!