I recommend putting the rings in a bag, box or other container rather than passing them loosely. It’s not that I don’t trust your guests and fear someone will pocket the rings, but I have seen one or two dropped during this ritual.
Officiant: Truly blessed is the couple who come to the marriage altar with the approval and blessings of their families and friends. (Bride and Groom) would like to take this moment to express their appreciation to you for being with them this day and thank you for sharing in the great joy of this precious moment. Their wedding rings are an external and visible sign of their internal commitment. During the ceremony we ask that you, who by your presence here today, are being called upon to uphold them in loving each other, take part in the warming of their rings. As each of you receive the rings please take a moment to say a prayer, make a wish or think a special thought about the shared potential that is their life together. When these rings come back to (Bride and Groom), they exchange gifts that can truly never be measured—your shared hope, mutual support and boundless love.
At this point the rings are handed off to the guests who pass them along until the ring exchange, at which point they always seem to miraculously appear back with the best man or ring bearer at just the right time. I’ve honestly never seen it ill-timed yet.