When Lily (3.5y) is very upset about something fixable, here's something I've found helpful:

L: Papa I don't want this cup! This cup is blue! I don't like this blue cup!

My first impulse is just to fix the thing:

J: That's ok Lily, here's an orange one.

If she's not very worked up then this will often work fine. She takes the orange cup and moves on with her life. But if she's pretty upset then I find this tends to continue like:

L: That's not what I wanted! I don't want that cup! That cup is too small! I want a cup like my blue cup but orange!

I think what's happening here is I haven't given her time to calm down. She gets the new cup, still feels sad and angry, and finds something else to be sad and angry about. And now she's gotten set on a kind of cup I don't have for her.

What I've found works better is moving slowly and being collaborative:

J: What would be better?
L: I want a different cup!
J: Let's go over and look at the cups and you can pick one out.
L: [chooses an orange cup]

This gives her feelings time to dissipate, so that by the time she has the new cup she's ready to enjoy life again. She's also the one making the decision, so I have buy-in from her and we're less likely to go in a direction that isn't fixing the underlying problem.