How to describe the face one makes - like pressing together of lips to form a straight line - when they feel sorry for a person but have no solution to offer? The kind of face that says, "sorry, mate. wish I could help." A phrase for it would also work.
I would use commiserative.
Feeling or expressing commiseration, compassion, pity or sympathy
–from Wiktionary, Creative Commons Attribution/Share-Alike License; via Wordnik
The first word that came to my mind was a "sympathetic" face.
sympathetic (to/towards somebody) kind to somebody who is hurt or sad; showing that you understand and care about their problems
Some actual examples from Google Books of this phrase being used:
His sympathetic face said she had a shoulder to cry on should she wish
– For Want of a Fiend, by Barbara Ann Wright
Suyana couldn't hear Grace's response, but Ethan made a pained, sympathetic face.
– Persona, by Genevieve Valentine
You could consider using apologetic which means the following:
Expressing or showing regretful acknowledgement of an offence or failure: 'an apologetic smile'
[Oxford Online Dictionary]
Ha made an apologetic face that said, "Sorry, mate. wish I could help."
Definition: pitying, sympathizing, showing a feeling of deep sympathy and sorrow for another who is stricken by misfortune, accompanied by a strong desire to alleviate the suffering.
Participants search for a compassionate face among a number of critical faces, which retrains the automatic, unconscious biases towards threatening stimuli commonly shown by people with mood disorders, according to the study published in Plos One journal.