Although Grimsby started the brighter, Macc bossed the majority of the first half, and the returning Nat Brown powered a header over the bar before Emile Sinclair stumbled when presented with a fine chance to snatch a goal.
Hamza Bencherif was denied a goal when his header looked to have crossed the line and Colin Daniel struck a post with a free-kick from the edge of the box.
The luckless Ben Wright thought he'd opened his Macc account but his strike 10 minutes before half-time was struck off by the linesman.
The Mariners had been reduced mainly to shooting from distance, Michael Coulson coming closest with a fierce hit that keeper Jonny Brain did well to tip onto the crossbar.
In the second half, Jean-Louis Akpa Akpro blasted wide for the visitors after robbing Macc defender Shaun Brisley and, at the other end, Daniel was denied a fine goal by Grimsby keeper Nick Colgan, who palmed away his close-range header.
Towards the end of a evenly-matched affair, former Stockport striker Adam Proudlock came close for Grimsby, firing against the post from six yards and his team-mate Jamie Clarke.
Three Macc players missed Ricky Sappleton's cross and Matty Tipton blasted over from a few feet away.
Five minutes from time, Sappleton shot wide when Bencherif slotted him in and the fixture ended goalless.
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