Some studies suggest that repid blinking & relaxing the jaw are some ways to avoid tearing up but there's no certainty it will always work.
Alternatively, opening the eyes as wide as they would go could help stop the tears before they even start. Focusing on bringing breathing back to a regular flow, counting to ten, taking slow deep breaths, and focusing on relaxing can have a similar effect. Looking up makes the tears pool slightly at the bottom of the eyelid so that they don't immediately run down the face. It can also help stop the flow of tears and get back to the right frame of mind. Tear ducts stem from the corners of the eyes down the side of the nose, so pinching the nose's bridge when the tears start to flow could help stop it entirely.
However, not all those tips are 100% effective all the time. It depends on the emotional intensity, stress levels one might feel in specific situations, and control over one's body and reactions.