There is very close proximity of Martial Arts training and Meditative practices. There is some common shared practices. For example there is a lot of breathing and movement. There are meditation / or breath motion Martial Arts like Qi Gong and and Tai Chi.
Studies have shown that Mindfulness practices increase the resiliency of soldiers, and reduces the risk of PTSD. The Navy Seal talk about the Flow State, the use a Box Breathing pattern to get into this state to clear their heads. The method goes like this breath in for 10 seconds, hold your breath for 10 seconds, breath out for 10 seconds, hold your breath for 10 seconds, repeat ad nauseum until you've relaxed your muscles and reduced your heart rate. Some of the most violent protectors on this planet are also the most emotionally intelligent.
Personally I like the practice of it has helped me a lot. When stress is high. I find Body Scanning and staring at a fixed point help. At a minimum most martial arts share the use of breath control and mindfulness and / or combining it with Mental Toughness. I've practiced with of the most ancient forms of Tai Chi, mindfulness in motion with breath control, and have been doing some research into Qi Gong. If you have ever watched the movie "The Best of the Best" about the Olympic Taekwondo Team they had a specialist come in and teach mindfulness / meditation.
Development a habit of mindfulness or practicing breath control can reduce stress. Like Sifu Paul Vunak says you have to have a game plan so when the adrenaline kicks in you have developed your fight or flight instincts to react. We talk about the OODA Loop, Observe, Orient, Dicide, Act. Through training we seek to bypass this because it takes the average person 10 seconds to respond. A train person can react with in the first second or two.
I find mindfulness reduces the amount of stress during a fight and helps with the recovery. Before I practiced mindfulness I would get shaky before and after confrontations. Now I'm calm for the most part.
Further...
If you look at most competitive sports like Boxing or MMA. Fighters will do some fast rapid deep breathing to oxygenate their lungs. If you look up Rickson Gracie and watch his Diaphragmatic Breathing (breathing through the belly, abdomen, diaphragm) it's pretty impressive. I've done Diaphragmatic Breathing for a long time. It's very calming, oxygenates your lungs, leads to mental clarity and mental readiness.
One reason I like Mindfulness is because you can do it with your eyes open in an aware state. You don't have to close your eyes and chant "om" to connect with the universe or calm your soul. As a Martial Artist being able to reduce stress, stay calm, be alert and have mental focus are important. That's why I prefer mindfulness. It is a good to have a specialist in this area.