The Fitting: A fitting can made to go inside the cavity of hollow objects to hold the piece. The advan...tage here is that there is no need to drill and it doesn’t need anything holding it on the outside. Sometimes it is difficult to get a fitting to hold the piece correctly which may require a good deal of tweaking.
Art Display Essentials also carries a few stock items that use this principle. The Center Post Base is simple and has a post for going up into the bottom of an item. They can be seen here: https://www.artdisplay.com/center-post-base.html
The Hat Stand also fits inside objects other than hats. They can be seen here: https://www.artdisplay.com/helmet-hat-stands.html
The Inlet: The inlet is sort of the opposite of the fitting. The base gets carved out and molded to the exact shape of the bottom of the object letting it fit down into the base and locking it into place. This is sometimes used in conjunction with other mounting techniques.
Backplates: This method uses clips to hold an object onto a backplate that could be black, clear, wood, etc. Sometimes the back of the object goes through the backplate itself.
Again 10-31 Inc. has been making these custom mounts for artifacts for over 25 years and will recommend which approach is the best for a particular situation.
Art Display Essentials also carries stock backplates in a number of sizes. You can see them here: