Great question.
One of my old T's and I were very attuned with each other's feelings. She also lead my mindfulness class and so we did a lot of work on just that. One time, during a particularly hard session, T shed a tear with me. Another time she ran her hand across my face to wipe away a tear. She was lovely.
I haven't really had anything like that with my current T ... but I think she understood how I was feeling when my 51-year-old Dad randomly had a stroke. She mentioned how her Dad had health issues too, and so she was particularly helpful to me during that stressful time.
I think that there is a fine balance that a T has to find between not feeling too emotionally involved in the stories we tell them (so they don't take them home with them and/or burnout), and being empathetic and providing us the support we need.
I am so thankful for my T(s)