I think most of the types react differently to their emotions, so part of the problem is that the expected response is different. I very rarely would cry where others could see me and if it happens, it's an involuntary response, not something that can be controlled and it is hidden by me as quickly as possible. If it is someone I don't know whom I am on my way past, I would rather them notice non-verbally (pat on the shoulder maybe, maybe not even that) and let me go mop up. If it is someone very close to me, the worst thing they could do is pretend it's not happening or try to cheer me up before the problem has been talked about. I usually need a chance to say what's going on, just have the person listen and respond supportively and then I improve rather quickly and can solve the problem myself. Maybe it depends whether the person is a thinker or a feeler...
I think one of the main things that makes you feel uncomfortable is knowing what is expected and feeling responsible to somehow fix the situation. In most cases, showing whatever expression of sympathy that comes naturally to you and the ability to listen with undivided attention (without offering solutions) is the most that is needed. You are not expected to do anything to actually fix things.
If you are somehow implicated in the problem, I don't know what works for other types, but for NFs, taking responsibility to bring it up (instead of hoping the other person will forget about it) will earn you all the points in the world. In that case, it is a matter of showing that having things right between you matters to you. In a romantic relationship, not expecting physical affection to resume until the problem has been resolved in some way, is also very important.