That won't do you any good if you are affected by magnetic variation, say local iron rich rocks which will distort both compass needles equally. This happened to our climbing party on Orizaba. We had accomplished the usual dark o' thirty early start and my companion was steering by compass. We were able to determine that the compass was off by more than 45 degrees, thanks to the presence of the Big Dipper/pointer stars/North Star brightly shining in the sky. The constellations are the ultimate authority; however, you can't count on them always being visible.

Aksar brings up a good point about featureless terraain where terrain features are absent or obscured. At the other end of the spectrum are situations where compass directions are irrelevant. Deeply incised canyons in the Colorado Plateau come to mind. When you are in one of those, the only directions of significance are upstream and downstream. What counts is a good topo map so you can look for possible ways out of the canyon (if that is what you wish). Sometimes even GPS signals can be deflected and degraded, giving an inaccurate position