Overall, there aren't many enchantments you can use that would be considered the best for shields in Minecraft. However, there are two that would be best to put on, and the first is fixing, the second is unbreakable.
Mending is a useful enchantment that will take experience orbs you earn from doing various activities and use them to repair your enchanted item when placed on an object.
For this reason, we recommend using it on the shield as you are required to fight monsters, so XP orbs could protect you longer with your shield in fights.
Related: Best Minecraft Shovel Enchantments
You can also, in turn, combine this with Unbreakable if keeping your shield usable is your goal in-game.
The reason for this is that the unbreakable will increase the durability of whatever item it's on, so if you place it on your shield, it will last longer. Then, when combined with repair, it will take less time to repair your shield via XP orbs.
Overall it's not very practical to enchant the shield, like if you have decently enchanted armor that would be good enough. However, if you want to enchant your shield, your best bet would be to use both of these enchantments.
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