In my new book, Turn Enemies Into Allies: The Art of Peace in the Workplace, a key element in the process is the leader's ability to center herself. As a manager, supervisor, or anyone caught in the middle of two conflicting parties, you must first manage your own mindset and emotions before trying to support others. Then, if you choose, you can coach others in the art and practice of centering.
It's a great concept, isn't it, to choose to be centered? To notice in the moment that you're off balance, and then decide to shift to a more centered state. If you know how you do this--catch yourself and re-center--you can easily coach others.