Hi RR
Flew last week on ATA with 14 TSA students - 7 of whom were under 16, no driver's licenses of course. The kids were all asked to show their ID, meaning the certificates. On the return trip, one of the boys had lost his - they immediately pulled him aside and sent him off with a security guard - out of my view and without my permission - I felt they should have waited for an adult to accompany them! He did return less than five minutes later - they just had him open his suitcase, and ran it through a scanner, then checked it through and gave him his boarding pass.
I didn't bring the original certificates - those are only needed for customs when exiting/entering the country. I just made a photocopy on the fax machine. I gave my daughter three copies - one for her pocket - one in her carry-on, and one in MY wallet. Better safe than sorry!
Most convenience stores have a photocopier if you don't have access to any other one - Good Luck and have a great trip!