So something I've been using more and more lately that I thought I would note (as personally I didn't really notice this for a long time). When you dig up an artifact in an AIs territory, it leads to a big penalty. The AI will pretty much immediately demand you cease digging. If you agree, the penalty actually drops to a meager -10....which in the grand scheme is not too shabby. This means that you can grab 1 artifact per civ without invoking a huge diplomatic lashback.