Listening is the key to remove the emotion from a difficult moment. Your tone of voice needs to remain calm and attentive to the communicators. The definition of communication is 7% verbal, 13% body lanuage and 80% listening. Many times by letting the parties talk it out in a controlled unemotional setting will create a constructive atomosphere to resolution. If possible all parties need to walk away with some feeling of resolve to their own issues. This may take more than one setting. You can create a step by step plan for follow-up with you as the leader.