The Bond of Matrimony is a ring given to the Dragonborn and spouse, one each, as part of the marriage ceremony. Wearing the ring has no effect on the marriage or spouse. It appears that spouses wear this item by default. The ring may be removed from their inventory if they are followers. Furthermore, it is possible for them to sell you the ring.
This item may be disenchanted by using an Arcane Enchanter yielding the Blessing of Mara upon destruction of the ring. However, there is no item that will accept this enchantment, so it cannot be used.