Damn, anon. You don’t ask the easy ones, do you? ;)
First, we’re going to have to assume there was a body. Until he had proof, I don’t think Garrus would’ve given up completely.
He doesn’t have a public breakdown, but his friends notice how carefully straight he carries himself, like he’s afraid a moment’s weakness will bring the whole house of cards crashing down. He doesn’t have time for that. There’s work to be done. People to help. A galaxy to rebuild. Shepard would want that to be the focus. He doesn’t laugh much. Once in a while Tali or James manages to coax a smile out of him, a brief flick of the mandibles that never comes close to warming his eyes. He inherits Shepard’s hamster. Odysseus seems unperturbed at his change of ownership, and Garrus finds himself hating a hamster for not caring more. Still feeds him, though.
When they get back to Earth, back to the confused forces of an army that never expected to win and have to deal with the consequences of what now?, he throws himself into work with fierce diligence. People ask about her. They demand words from him like he owes them his memories, like they own her because of what she did. He’s polite to civilians, mostly. The media learns quickly not to bother him. He walks fast, with his head down. His shoulders begin to hunch under the weight. Tali tries, once or twice, to get him to talk. He only looks at her, wounded, and grates, “Not you too.”