The general rule (atleast for Fender tube amps) is that a 50% mismatch is tolerable. If the output impedence of the amp is 8ohms, then either a 4 ohm cab or 16 ohm cab will work OK (with some loss of power and frequency response).
Too much of a mismatch is a problem, even if it is higher than the recommended load. For example a 16ohm cabinet is NOT recommended for a 2 ohm Super Reverb amp.
Marshall amps are much less tolerant of mismatches from what I hear, but often come with impedence selector switches. I would not try running a 4ohm Marshall with a 16ohm cabinet.
Good luck.