Empathy is the word usually used...
Put yourself in their situation, see things from their point of view - it certainly helped me through a lot of situations...
I've never been c/c - I worked in the rail industry as a train conductor, which is a similar job in many respects, being responsible for the safety of passengers, as well as being THE only visible member of front line staff when it all goes wrong!
It doesn't always get easier, but 'putting yourself in their shoes' is certainly a very good starting point...