Paul Hurst's first match in sole charge for Grimsby after the departure of co-manager Rob Scott ended in a dire goalless draw at Chester.
Joe Colbeck was given a straight red card for the visitors just four minutes into the second half after reacting to a challenge on him by Michael Kay.
Ben Mills and Alex Titchiner had chances for Chester, but they did not seriously test keeper James McKeown.
The Mariners struggled to create chances as the game petered out.
VIEWS FROM THE DRESSING ROOM
Grimsby Town manager Paul Hurst told BBC Radio Humberside:
"I'm pleased with a point because of how the game went, with the sending off so early in the second half.
"I thought just towards the end of the first half, we finally looked like we were getting into our stride and playing a bit better so obviously I would have liked to keep 11 on the pitch.
"I thought we coped extremely well with it, and it's credit to the players work rate and commitment. "