I had this discussion recently with another facilitator. Like me, she was able to handle conflict in the room. Like me, she hated it and wondered if there was a way to be more confident, more balanced, more able to handle the conflict without paying the price.
Maybe there isn't. Maybe part of the price of leading - as a trainer or facilitator, as a manager or executive or team captain - part of the price of leading is the slightly sick sensation that follows conflict. The feeling that comes when you can't shake the idea that there was something you could have done better, something that would have outframed or out-manoeuvred the conflict.
But it's entirely possible that paying attention to people's anger or frustration requires that you meet them in that level of tension and uncertainty. And the shaking that you do afterwards, with your own anger and frustration and uncertainty, is the sign that you were really paying attention, that you took the conflict seriously. This is not the same as giving up your own point of view, and it's not the same as making a mistake. It's more like building a bridge through a bog - you'll probably get muddy making your way across.
It's not necessarily harmful, this aftermath. It pushes us to look for ways to agree instead of arguing, which is good. It gives us a stake in how we make other people feel, which is also good. It may even give us insights that we couldn't get if we stayed as cool and comfortable, as confident and as competent as we wish we were.