Usage patterns
〈相手〉とペアリングをするto wear matching rings with someone
We decided to get matching rings with my girlfriend to mark the occasion.
ペアリングをはめるto put on a couple's ring
The two of them are wearing matching couple's rings of the same design.
ペアリングを交換するto exchange couple's rings
We exchanged couple's rings for each other's birthdays.