When an artifact wish fails due to the artifact already existing, communicate this clearly to the player, and then let them use the wish for something else.

Remove the random element of artifact wishes. In each game, you can either wish for one quest artifact, or up to three non-quest artifacts, which you are guaranteed to get on the first attempt. Artifact wishes beyond that will always fail.

If an artifact has been generated and is on some existing level, wishing for it will remove it from that level and teleport it right into the player’s hands. However, the beatitude, enchantment, and other fields of the wish will fail.

Intentionally destroying an artifact, such as by eating it, reduces the artifacts generated counter and unsets it as having existed, so you can wish up or be gifted new (or even the same) artifacts. Possibly do this whenever an artifact is destroyed, including by accident.

Failed artifact wishes give you the base item type instead of nothing.

Wishing for an artifact drains two charges from a wand of wishing. If it’s a wrest wish or from a source that only gives one wish like a djinni, you merely get the base item type instead.