There is not really one company that provides the best mediation services. The first issue is whether this is mediation in e.g. a domestic context (e.g. child custody), or if it's a regular civil matter (e.g. car accident case). The next issue is finding a good mediator within that area of law. Many good mediators work in very small law firms. There are some organizations of mediators also. Lawyers typically know the best mediators in their local area. One looking for a good mediator, without a good source for a reference, would simply have to do some research.
There is not really one company that provides the best mediation services. The first issue is whether this is mediation in e.g. a domestic context (e.g. child custody), or if it's a regular civil matter (e.g. car accident case). The next issue is finding a good mediator within that area of law. Many good mediators work in very small law firms. There are some organizations of mediators also. Lawyers typically know the best mediators in their local area. One looking for a good mediator, without a good source for a reference, would simply have to do some research.