The best strategy for dealing with an upset ENFP:
Let them say what they want to say so they can get it out of their system.
HUGE DISCLAIMER: This is NOT to say that they should they be given free reign to say and do whatever they want.
The fact is that ENFPs are NATURALLY very EMOTIONALLY EXPRESSIVE---so if you judge the intensity of their expressions by the standard of a relatively stoic or serene temperament, you are likely to underestimate their overall reasonableness.
They're not likely to go apeshit if they are heard.
More often than not, they will feel satisfied that they were allowed to say how they feel--even if the problem isn't going to be resolved.
If you don't have time or just aren't up to it at the moment, assure them that they will have an opportunity at SOME point to express themselves, or allow them some form of communication with you, such as email, letter, phone message, etc. so you can deal with it if or when you are ready.
If you don't like what they say or the way they say it, keep in mind that arguing with them will only make things worse.
The ENFP isn't nearly as concerned about "being right" or even solving the problem as one might assume.
ENFPs are INFORMATIVE rather than DIRECTIVE, meaning that they prefer to provide information and let others decide what to do with it, rather than directing the actions of others.
They mostly just want to express how they feel.
If they feel that they are being dismissed or silenced or told they "shouldn't" feel they way they feel, they are likely to resort to extreme behavior in order to make sure they are heard.
NOBODY wants this to happen. Not the ENFP or anyone else.
The more you dismiss them or try to silence them, the more problems will result in the end.
NOTE: This may apply to other types as well (and I suspect that it does), but I don't feel as confident speaking for other types.