Creating agreement--if two people can agree about how they will engage with each other IN the conflict, it often helps them to work through it. For example:
We will have an open mind
We will take turns listening to the other
We will test assumptions by speaking directly and openly
We will not judge each other's weaknesses based off of our strengths
We will not interrupt the other person
We can agree to disagree
A facilitator can help the two create this agreement together--it is something not given to them to follow but co-created by them both. Once they agree on how to talk, the conflict can usually be worked out. Most conflict has to do with communication issues more than anything else.