When we encounter a potentially threatening situation, a lot of times we lack the confidence to handle it any other way except for the fight or flight method. But one of the most useful tools anyone could have in preventing something from escalating into a possibly violent conflict, is the ability to de-escalate the intense flow of emotions of those involved. Remember, both of the parties will have a much better chance of getting their needs heard and goals addressed if everyone can first discuss things calmly and in an organized fashion. Let there always be a turn for someone to speak, and those listening should also be able to calmly disagree if that is the case.
But where do you even begin in learning how to chill out folks who may even have angry, flushed faces? It can be very intimidating at first, but being observant is the first step. It will help to know the habits of a person when they are nervous. The sooner you can recognize signs of anxiety in its beginning stages, the better. If you cannot understand exactly what it is important to that person, then asking clarifying questions (not telling him or her what to do) will help so they know that you really are listening and paying attention to his or her needs.
In any case, preparing for a potential crisis before it happens will be the most beneficial. Especially having more than one of you to mediate will mean that attention to give will not be in short supply. Thanks for reading and have a great day.