Wow, I totally understand your frustration as I am also in this situation many times. Unfortunately, there is no magic solution, as all shows are different and as artists, we never know exactly how the judges are going to determine their winning choices, or what exactly they are looking for (and sometimes it's just politics). First, check the award criteria. Does it give you all of the necessary information? If not, take a moment to give the promoter a courtesy call and ask them outright how they would prefer to have a contender display their entry, if there is a special form that needs to be given to the judges before the show and if any special labeling is preferred.
Personally, if I am entering a piece into a show competition and there is no specific display area for the entries, I display my chosen item or set in a separate display box, with excellent lighting, in the front of my booth. I chose a background color that makes the item 'jump' and add a plainly written card that describes both the materials and the process used to create it, as well as its name/title. If it is an unusual item, like a specialty headpiece, I also add one nice photograph of it being worn, so one can see it in use.
If you do not win a contest or judging, be sure to look over the winning entries to see exactly how the artists presented their pieces and take a few minutes (while congratulating them) to ask them how they think they won.
Whatever you do, do not stop entering contests! They can fuel your imagination and hone your skills. Best of luck in the next one!
Answer contributed by Dale "Cougar" Armstrong