I have three nests in one of my glass cases with lots of other natural world stuff collected over a lifetime. I bagged two of them while there were live residents within. I put the bags--heavy contractor type bags-- in Tupperware and then into a freezer for a month or so. None came back to life. They're cool things, the nests.

https://hortnews.extension.iastate.edu/preserving-and-displaying-hornets-nest