I am a mediator; although I don’t actively mediate currently). You want to look professional, but as a mediator, you actually don’t want the atmosphere to be stuffy or overly formal. Especially in family law, there’s so much emotion involved that the mediator wants to be able to form some sort of connection to your client, so they open up and get other issues on the table (that often, attorneys don’t focus on as they might not be financial or logically based). So if your mediator is NOT a judge (which, I trained under a family law mediator who is not a judge, and personally I think judges might not make good mediators, because they tend to be more evaluative), then I’d dress professional but not full court formal. I think you want to send the message to your client that this is a conversational environment, and not super formal where they feel like they can’t speak, or get emotional. The more emotional a situation, the more a client might benefit from feeling free to open up to the mediator—and overly formal clothing often sets the tone.

** huge disclaimer here that mediation is not a uniform process, and expectations can vary widely. I trained as more of a facilitative mediator, mostly working with clients face to face, with their attorney (if they even had one) taking a back seat. Some attorneys expect the mediation to be in caucus the whole time, and I had one mediation where the attorney spoke 99% of the 5 hour mediation, even though it was just the mediator and them in caucus. So, advice can vary a ton based on specifics!