When looking to defuse overly emotional and confrontational situations, you can use your non-verbal communications to help subdue the other party.
Rather than standing face to face, shift your positioning so that you stand
shoulder to shoulder.
Turning your feet away from them slightly will help you
appear less intimidating and confrontational. Tilting your head will make you
appear like you are listening, which will help them begin to do the same.
Slowing down your vocal speed and dropping your volume will also help to
de-escalate the situation.