Crying is not a failure of composure. It happens when something matters more than the machinery for handling it, which makes it a measure of depth rather than of weakness, and it communicates in a register that words cannot reach. Grief, remorse and love all arrive this way when they are large enough.
If you have been holding something back, you are allowed to let it out somewhere safe, with a person or alone. And when someone cries in front of you, resist the urge to fix it. Stay, say very little, and let it finish on its own.