We've never registered jewelry but we were subject to a random customs search once. The inspector didn’t seem to care much about Mona’s extensive jewelry collection but he was fixated on a knock-off Cartier watch I bought for $25 in SoHo. He must have spent 10 minutes looking at it and questioning me. I kept trying to tell him it was a cheap knock-off but he didn’t want to believe it. He thought he’d scare me by telling me if it was an imitation he’d have to confiscate it. When I said OK take it, he lost interest and let us go.
I would suspect the burden should be on Customs to prove you bought something outside the US and are trying to smuggle it in. It’s a little different with expensive electronic equipment where a carnet may be necessary. Tom.