Emergency self empathy is simply stating what you value (need). I usually say this silently to myself, although stating it out loud (when by myself) is very effective too. Here are some that are common for me:
When parenting kids that are yelling at each other "I really value peace and cooperation." When I am interrupted when speaking in a work meeting, "I really like to be heard." When a judgmental thought that says I am not a good parent crosses my mind, "I love competence as a parent."
Emergency self empathy allows me to return to a calm enough space to recognize what I am longing for.
When I first learned about NVC, I focused more on getting to the request when I was triggered. Self empathy is part of the four step process. Over the years, I have begun to deepen the practice of self empathy and recognize how much it helps me return to a calmer state of mind, body, and spirit. We are more likely to make a request rather than a demand when we come from this space.
I use this part of the process frequently, and it helps create a sense of fullness of needs in the moment even if I choose not to engage the rest of the four step process.