Sometimes no words are necessary, use you body language to convey that you are "present" and supportive. For example, enter the room with a calm neutral expression (hardest part IME), make brief eye contact, slight nod of head "I acknowledge you and your feelings and am here with you ". Do what needs to be done, sweep the room with your eyes again and quietly exit.
I love this video on the very important difference between sympathy and empathy, it was a part of a lecture I attended on therapeutic communication.
Brene Brown's video on empathy vs sympathy