Here are a few of my favourite frames for silhouettes. The Victorian lady (above, middle) accepting a flower from her little daughter is held between two sheets of glass that slot into a thin metal frame. The effect being a transparent background which gives the silhouette a contemporary feel. Below the man’s bust is held simply by magnets between two slabs of perspex.
Ovals are a nice shape for framing individual silhouettes. If you can’t find an oval frame a rectangle frame with oval mount is equally fitting. Oval frames were popular for framing silhouettes in Jane Austen’s era but due to production costs are becoming less common in high street frame shops.