When you wish for an artifact that already exists and fail to get it, the game should either hint at or outright tell you the location where the artifact was generated so you can go track it down.

Do this by saving the X, Y, and Z coordinates at which the artifact was created when it gets generated. If the artifact happens to get uncreated, like as part of level generation, the saved coordinates should be reset, because the artifact is then able to be generated again.