My brother failed a bunch of students for cheating. He got lots of heat but stood his ground since he had absolute proof. He won in the end.
Good for him. You have to get your ducks in a row with these things. Gather your evidence and talk to key admins before the parents are notified. I usually won my battles, but I learned to be selective about them. Mostly I worked with natural consequences. Students who cheat on homework usually test very poorly, so they make their own punishment. I didn't give a lot of credit for homework and monitored test integrity like a hawk. Worked for me, for the most part.