Try making a few calls before the important one to break the ice a bit. Another trick is to start the conversation in an unconventional way, so you don't have time to predict what you're going to say (and anticipate the blocking).

What really worked for me was to force myself to _never_ replace words and to accept that I will stutter at times.

I also have a silly trick for overcoming a prolongation. When I'm stuck, I voice the first sound of the word, then take a short silent rest, and continue with the rest of the word. For instance, "f...ailure". Knowing that I can plough through any prolongation and still be understood has reduced them tremendously and lowered my anxiety. I'm not saying this trick will work for everyone, and I haven't seen it in any of the books.

Unlike the author, I think there's nothing wrong with apologizing for a stutter. That's a useful tactic because it brings the issue out in the open, instead of putting all that effort into hiding it. I'll apologize in advance, just to lower my stress level.

Edit: Renamed block to prolongation.