Despite the fact that the player character can equip the ring regardless of attire worn, the wedding ring serves no actual purpose whatsoever, however the ring will appear on the Sole Survivor's finger while wearing certain armors if the ring is equipped. The Wedding Ring is the only ring that can be acquired in the game and cannot be modified.
The texture reveals that the inside of the ring has the text "Love, honor and cherish" engraved.
If choosing to reject the confirmation process of either MacCready or 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 if it's 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.