This is a very good question as a suggested topic. While it may be possible to write extensively on it, I will give several examples.
I recall when I was about 18 years old, and had been practicing aikido for about a year or two, my teacher developed an exercise where he would attack with a wooden sword and we practiced evading it. As a Vietnam vet, I think he wanted to impart something he experienced while facing his fears during 2 years of combat. So one day he picked up a real samurai sword and began attacking us with that during these exercises. Slowly, he built them up to the point where I found him attacking me 7 times in rapid fire movements at full speed and with full commitment. He did not have the experience or control to train people in this manner, and we have disagreed on this practice he developed ever since. However, on the last sword cut, I realized I was too late to evade the attack. I immediately felt panic welling up. However, at the moment I noticed panic develop, I had a powerful reaction to it: I knew panic = death. I shut it down instantly and began an evasive move. After I began to evade the attack, again, I knew it was too late. I recall seeing that the sword was going to cut off my right shoulder and arm. I thought there was a hospital across the street from the dojo so I would be alright, but then I realized I would not even live to get to the hospital. There was nothing left to do, so I relaxed and waited for my fate to complete itself. What I did not realize was that at the very moment when I shut down the panic and began to move, my feet went into the air and my movement continued. As I watched the sword come down to slice off my shoulder, my shoulder continued to move out of the way from my initial reaction. One could say that the sword practically shaved the hair off my chest rather than slice off my right shoulder. I remember how my face became pale and my knees began to shake. My instructor was also quite shaken up as well. I tell this story to highlight a method of staying calm in an attack. To the extent one learns the lesson that fear is self defeating through awareness, one will learn to cut off the reaction and do what is necessary constructively. In my case, this situation was an example of plain dumb luck, I was not aware so much. But I use it as an example that can help others realize the importance of cutting off one’s fears through awareness and then returning to appropriate action a hand, an important tool in staying calm during a violent situation.
In point of fact, the entire practice of aikido is a method to help one remain calm during a violent situation. We practice having someone attack us. We learn a movement. We practice it over and over until muscle memory takes over and the calculating mind dries up. We focus on closing openings by being aware and relaxed. Our partner should, in a non-combative way, show us where we are open during regular practice so we can close each opening over time. Then we practice defending ourselves in more pressured situations where numerous people are attacking us simultaneously. We learn to become relaxed and aware of our entire environment, so we can perceive sneak attacks, etc. Through awareness during practice, we learn to calm ourselves down and become more efficient, and importantly we learn that this is critical in making our efforts effective. We also perform during tests so people who feel that environment as pressure will learn to relax while coping with it. All these forms of practice lead to a substitution effect: when an emergency situation develops, rather than become tense, we are relaxed, aware and react reflexively based upon muscle memory. This practice is called takemusu aiki, or the highest form of practice in any martial art (obviously with different names for each art, but the practice is the same).
For some people, learning to concentrate on their center of gravity is a useful form of practice to learn to control their fears. The center, or hara, is an infinitesimal point about 2 inches below the naval. We practice learning how this center is a receptacle where we receive ki and allow that ki to flow from there. Ki flows freely and should not be obstructed, but it is also not something “special.” Like air, it is everywhere and ordinary. This is not a method of training we regularly use in our school, but it can be a useful to help people learn to control their fears and remain calm.