I can't think of any references to them either (which doesn't mean there aren't any!) but I assumed the trial rings were part of Tolkien's idea to create a plausible mythology for England. Magic rings are part of folklore:
http://en.wikipedia.org/wiki/Magic_ring
and I supposed that these lesser rings gave the rings of the myths of the real world a Middle Earth origin - just as the lesser sprites. spirits and fairies of "true" folklore can be reconciled to the houseless Fea of elves who refused the call to Mandos at death or to the lingering diminished elves faded almost away.