I work as a programmer. My husband works as system engineer. He is on 24/7 support if our customers' websites get attacked. We promise zero downtime to our customer. We cannot let the website down for any second.
My nature is totally different from my husband's. :) I have high level of anxiety. In the past, I couldn't even demo the product in front of the customer.
When the website got hit by the bot and it died, my husband remained calm and fixed it.
If I were him I won't be able to do that easily. But, yeah, I can be better and better. Many books can explain about this and also provide an answer of can people improve on managing themselves in crisis situation. I read "The unthinkable by Amanda Ripley". It is really a good book.
Being calm in difficult situation is naturally genetic aspect. People can do better and better when they train themselves in such situation again and again.
I would suggest 2 things:
You set your goal how you want yourself to be. You want to keep calm in a difficult situation? Keep that in mind. Think about it, do it. Setting clear goal helps you reach your goal quicker.
In the situation, spend sometimes to imagine that you're not part of the situation. Imagine that it's just another story your friend's telling you. And you will give him/her an advise that he/she does bla bla bla.
Because normally when people are directly related in the situation, they will lost big picture and also think of the worst case scenario. It's hard for your brain to have a good idea in that situation. And you can also be distracted thinking about the consequences.