This one was originally suggested to me by Shinali, though I’ve elaborated on it a bit.
For this characterization exercise, you’ll need two characters who, if they were to run into each other in most contexts, would be at each other’s throats—physically, verbally, or otherwise. They don’t necessarily have to be from the same world, but it would probably make it easier to make sure that their default mode is hostility.
Once you’ve got them, put them in a situation where they are required to be civil to each other. Coming up with the actual situation is part of the fun; it contextualizes the resulting scene, and what it is that’s causing them not to fight says something about who and what they are as well. Is it because there are witnesses involved? Have they gotten orders from people they respect? Do they consider themselves bound that hard by local courtesy, or oaths to behave? Is there some sort of magical compulsion in place? Are they both refraining from conflict for the same reason, or do they each come in with different reasons to keep their hands and their more obvious insults to themselves? What exactly are they forbidden from doing?
Having figured that out, write the resulting scene. How do they handle the situation requiring them to behave? What sorts of workarounds do they come up with for it? Do they respond with truncated sentences, backhanded compliments, subtle (or not-so-subtle) attempts to get the other one to start it? Is there a difference in skill between them when they do that? What happens to their character dynamic when fighting isn’t an option—or is it just delayed for when they don’t have something else influencing them? (If you’re feeling really ambitious, would any of these answers be different if they were refraining from conflict for different reasons?)