Thinking back to when I've been told to calm down, if I did in fact calm down, it was not those words that were helpful. It was the tone of the person's voice, their care and concern. It was the comfort they offered when they saw that I was upset.
Instead of "calm down", what about saying "I can see that you're so upset/mad/sad/frustrated/angry/embarrassed (whatever feeling you recognize, you label)" or "is there anything I can do to help you" or "I'd be really (insert emotion you notice) too if ______ happened to me". It feels so good for anyone to get validation for what they're feeling, kids included.
You can double the impact by also offering support in ways that are not words such as hugs, kisses, covering them with a blanket for comfort, offering to grab a favorite toy or a snack, offering to cuddle until they feel better, suggesting a bath, creating a quiet space or time out for them to get calm again.
What works for your kiddos to get calm when they're really upset? What works for you?