Some Monsters carry special artifacts around with them which are not found anywhere else. These artifacts are only worth a little more than normal ones so they are not anything to get excited about, but they are a nice surprise for a hero. If a monster has an artifact associated with it, it will always give it to the hero when defeated in battle.
List of Monsters' Artifacts
How to recognize
You cannot recognize them because they appear to be normal artifacts. However once you have seen your hero write about getting a certain artifact always from a certain monster, you will begin to get an idea.