Metal plate stopping a 19th century bullet?

Let me preface this by saying I know nothing about firearms, old or new.

In Back To The Future III, Marty stops a bullet from killing him by wearing a piece of iron from a stove (I think; it’s been a while since I’ve seen the movies). Would something like that really work with some sidearms from the 1800’s? Or was it typical Hollywood stuff?

If it could work, I imagine it would be dependent on caliber and type of weapon? How thick would a metal plate need to be to stop, say, a Smith & Wesson .44?

If none of this makes sense, feel free to tell me and I’ll try and re-phrase it.