Baggage reclaim with an international flight

Assuming that you've purchased a single ticket for this trip (instead of going to United and buying two separate tickets), your checked luggage will be checked through to Edinburgh, and you will not need to claim it at Newark or anywhere else along the way.

Note, however, that if you take the same route in reverse on the way home, you will need to claim your bag at Newark when you go through US Customs. After you take it through Customs, there is a baggage drop where agents will take your bag back and return it to the system; you'll find it again (barring any mishaps, of course) when you land in Milwaukee.