I had read about gaffer tape (essentially a thick cloth tape used by stage hands) as a way to protect terrain board edges. For the hell of it I bought some on Amazon a couple months ago and had my first opportunity to use it on a diorama board.
I, of course, didn't take any pictures but I have to say it:
1. was very easy to use
2. looks really nice - I did a black tape directly on pink 2" styrofoam
3. can be cut to cover contours of hills or other elevations
4. has a nice texture - "richer" feel/look than say black duct tape or painting the edge of the boards
This was the one I used if anyone wants to experiment with it:
https://www.amazon.com/gp/product/B01M63LTTU/ref=oh_aui_detailpage_o09_s00?ie=UTF8&psc=1