What can be ineffective about saying "calm down", "you don't need to feel that way", or "don't feel like that", is that people don't generally enjoy feeling like crap, so if they knew how to calm down or stop, they certainly would. It is like telling a person with the flu to "chill out and quit throwing up" or "relax and quit having a headache". Such statements are often received with deepened frustration.
Treat the emotionally overwhelmed person in the same way you would treat a physically overwhelmed, ill person. Provide simple things that are made to help them feel better. Ask the person what they need to feel better. Perhaps say that you feel badly seeing them feel badly and would like to help, etc. without taking a superior role that implies their state is completely their fault and choice. People are much more complex than that and there are always cause and effect reasons for the way people experience life that are deeply compelling. Remaining calm, not allowing emotion to escalate, treating the person with respect, gently guiding them towards more correct thinking as they appear ready to receive it, are all typically effective strategies.