The Sole Survivor can equip the ring regardless of attire worn, but it serves no purpose other than decoration. Although most pieces of armor cause the ring to be hidden, the ring will still be visible on the Sole Survivor's finger while wearing certain other pieces of armor. The wedding ring is the only ring that can be acquired in the game and cannot be modified.
The inside of the ring has the text "Love, honor and cherish" engraved.
If choosing to reject the confirmation process of either MacCready, Hancock, etc., by saying the Sole Survivor still loves their spouse when passing the Romance speech checks while wearing the ring, it will alter the responses slightly. However, the effect is the same regardless of whether the ring is equipped or not.
Can be given and equipped by a companion (except for Dogmeat and Strong) but it will not have any extra effect.
The wedding ring has no use other than being a reminder of the Sole Survivor's dead spouse.