Maintaining Reference To Object?

My program references a specific object that is contained in a list. The references point directly to the object itself, instead of its position (index) in the list, since that might change over time as other objects are added/removed. However, occasionally this object is edited, and (behind the scenes) this sometimes involves replacing it with a newly-created object (so the code looks like ListA.item(i)=new testobject...). In which case, if my understanding is correct, all the program references to this object are no longer correct, since they point to the replaced object instead of the new one. So I'm wondering how to maintain the integrity of the references, since the list index is not permanent, nor is the object reference technically permanent. Should I create some ID number for the object, and maintain and use it for references (so the new object would get the old one's ID)?