Another very common way of scoring certain moments in movies are so-called “Red Herrings”. This principle is used for instance in tension scenes where you musically build up to something that DOESN’T happen.
A classical scenario would be a woman walking through a dark basement, hearing a noise behind some corner. She walks slowly towards it and in the moment where she looks around the corner we and she see(s) that it is just a plastic bag in the wind or something other harmless resolving the tension completely. Still it works very effectively to score that scene according to HER emotions. She probably expects something scary behind the corner and supporting this with music of course helps the tension.
As a word of caution it should be mentioned that scenarios as the described one above have become movie and scoring clichés. Particularly excessive use of it can become silly and really annoying so its use should be limited to the minimum to keep the effect. Of course, if the movie you are scoring sets up several scenes exactly like this, there’s hardly anything else you can do than to go along with it but if the scene is less “on the nose” and you have options to score it differently, you should prefer a less clichéd approach in most cases.