[lawump]

As a professional umpire we were always, always drilled to "keep the game moving". As a result, we were taught that if you knew that a coach was coming out to the mound specifically to talk to YOU (as opposed to his pitcher), then we were not to wait to break up the conference. Rather, we were told to go to the mound and get it over with.

And in that situation I would:
(1) tell the manager "ok, let's go" (which would be immediately followed by comments about my strike zone).
(2) give the manager his warning about not arguing balls and strikes OR if his first comment was personal (for example, "your brutal today") I would eject.
(3) If the manager was only given a warning in step 2, then I would eject if he continued to argue without leaving the mound.

As for situations in which I did NOT think the manager came out solely to argue with me, but actually wanted to talk to their pitcher, I would handle breaking up a mound conference pretty much like pdxblue suggested...the only difference being that sometimes some managers did come out to only talk...and not only when they wanted the pitcher removed...so I wouldn't be quite as quick to go to the mound when the manager makes the trip.

As an aside, I have, fortunately, yet to have the situation where I thought the head coach was going out to the mound solely to talk to ME arise in any amateur game I've done since leaving the pro ranks.

I will also tell one war story of my most memorable conference at the mound. I will say, first, that I was having a "rough" day behind the plate (and I'm being generous). Anyways, the Red Sox affiliate's manager Dick Berandino came out for a conference at the mound...and I KNEW he was only coming out to have words with me.

So, when Berandino got there and started scraping dirt of the pitcher's plate without saying anything to his pitcher or catcher, I immediately started out to the mound by walking with deliberate speed.

Halfway to the mound, the Sox's pitching coach yells, from the dugout, "Blue, you're f***ing choking out there," while bringing his hands up to his throat. I stopped and immediately ejected him. He came sprinting out of the dugout, and I had no doubt he was going to run up and bump me...when Berandino, whom I believe is a former college football player at Holy Cross, grabbed his much younger and much bigger coach (who was sprinting) around his waist and stopped him. He yelled some more profanities and left.

Berandino just said, after the coach left, "you have to expect to take some when your missing pitches that much." I just said, "skip, I understand...but I ain't taking it from any assistant coach." He just left and we moved on.