My standard packaging is 35mm film canisters. Most things are small enough to be wrapped in a little bubblewrap and then placed in a canister which is then put in a bubble-mailer. Making friends with the staff of a photo processing shop ensures a steady supply of these - as long as digital photography doesn't replace film entirely.
However some things do not fit into a film canister and improvisation is called for.
I have found that very strong heavyweight card postal tubes cut into suitable sized sections or cores from packing tape etc. make good containers. I cut thinner card circles and glue one on what becomes the base, wrap the miniature(s) in bubblewrap and then add a lid circle using adhesive tape to hold it in place, I mark it to indicate to open this end.
N.B. I use my scroll saw to cut the long thick card tubes into sections.
My new iron weight holding a shallow card core from adhesive tape securely while tacky glue dries and the finished container about to have the lid secured.
The finished and sealed 'box' is wrapped in bubblewrap for extra protection and to help prevent it from splitting through the bubble-mailer. When I send several items in film canisters in a bubble-mailer I will use bubblewrap to keep them together and help prevent damage.
When I have a quantity of miniatures to send these are all carefully wrapped individually in bubblewrap and packed into a strong box.
While these methods of packing may not be pretty they are very practical and I hope it may provide some ideas on how to solve the problem of sending a dainty little miniature to the other side of the World and have it arrive just as it was when it left you.