Conflicts arise for many reasons, and in some situations disciplinary action is indicated. Is one party clearly at fault? Is their behaviour entirely unreasonable or inappropriate? Is anyone in breach of contract, or their terms and conditions of employment? Just because two people have a disagreement does not make it of equal responsibility.
Distinguish whether a difficult situation is one in which the parties simply cannot find common ground, or if investigation as to whether one party is at fault is needed.
Sometimes people simply cannot find common ground and resolve their own differences. If you can assure them that a good win-win resolution can be found, providing they are willing to co-operate with you (not initially with each other), then you know mediation can really work.
Mediation is voluntary, and encourages people to be reasonable with an intermediary who will listen to their story.
Speak to each party involved on their own. They must know that if you are to introduce an uninvolved mediator, there is no chance of an initial bias or preference. If they know there is no blame game, only a desire to avoid confrontation and understand their situation, they will be more ready to participate.
An independent mediator is not a guarantee of your preferred outcome, but it is a fair means towards the best possible outcome.