My experience here lines up with the experience cited by others on the thread.
To phrase what seems to have worked for me in a more systematic manner -
A. Micro level - deep breathing helps. At the end of a long day, when I am fatigued, my words get slower and harder to get out clean. I take a deep breath or a series of breaths and this usually helps.
B. Marco - meditation really has helped me deal with my own thoughts and insecurities ( which unfortunately stuttering tends to push more of), and find a core of Calm. The more I reconnect with that sense of calm, the more I feel like stuttering is within my control, and the more it helps.
Wouldn't wish it upon anyone - many days ended with me cursing and hating myself. Many days I would blame my father for it (easier to blame him, as a young boy) for not doing anything about it.
I would certainly hug every little kid I see with a stutter. Not just for what they are going through then, but to just let them know that "it will be OK".