Here’s a photo of one of the moth mating cages I put the Luna female in. I make these out of plastic snow fencing sold at most hardware stores. These are super cheap and work fantastic for the larger moths (i.e. Cecropia and Polyphemus). If your Luna is on the large size (northern genetics?) they won’t usually squeeze thru either, at least not until they’re mated and un-couple (the next evening).

Mating moths can be a real pain. Some are very particular about their mates and the timing. All are prime food for birds. To avoid the birds I put my cages up in the trees at dark and set the alarm clock to go off before morning light to retrieve them. Dang birds get up VERY early!
If you’ve got a mated pair you have to very carefully carry the cage into a structure (barn/shed/house) for the day so the birds don’t get the moths. If you’re not careful, or trip, the moths will uncouple and you may end up with an unmated female.