How can I calm panicked units?
I'm playing Ironman Classic and just lost one of my rookies to a plasma pistol in the face. Both of my veterans started freaking out, and shooting at random people.
Is there anything I can do to calm them down before they kill each other?
Panic is a one-shot deal. When a unit panics, they react erratically, and lose their next turn.
This means that, in a best case scenario, you will regain control of the panicked soldier on the next turn.
However, XCOM being what it is, your soldiers may panic again (the lowered will from having already panicked not helping), with the same unpredictable results.
Late game, the psionic ability "Psychic Inspiration" will remove panic, and re-allow them to take their actions. If cast preemptively, it can often prevent panic from happening in the first place.