I loved my meditation based stress reduction class (MBSR) and it helped me a lot to use mindfulness both in and out of therapy.
For me sitting with my emotions can still be challenging and hard but I can do it more and more comfortably, regardless of the type of emotion that it is (because I only want the "good" ones and I really want to avoid the "bad" ones).
There are also types of therapy that lend themselves to learning mindfulness. Actually the woman I took the MBSR class from uses it all the time in her therapy. Some of the somatic therapy groups use it too. I have been fortunate to find a therapist trained this way and it has made such a difference in my life.
PS After two weeks of meditation (or the class) they already start to see brain changes in those that meditate.