For the mirrors, I laid them down on the ground and shot from above, at just enough of an angle so my camera wasn't reflected in the mirror. I then got down on my knees and shot from the side, basically trying to get the detail on the mirror. I may try this again with a different colored background, now that I know it's going to work.
For the glass framed artwork, I hung a see thru sheet across the dining room window, sat slightly off to the side of the sign and snapped from that angle. They're not perfect, but they just might have to do for now.