Grimsby's Michael Coulson then brought a fine one-handed save out of Scott Brown with a right-footed strike as both sides traded chances.
There was drama in the last minute of the half when referee Paul Tierney adjudged that Michael Leary had fouled Richards in the box. And the striker took the penalty himself but fired the ball against the bar.
Cheltenham had defender Ashley Eastham, booked in the first half, sent off for a second bookable offence after 56 minutes.
But keeper Brown kept Grimsby at bay with fine saves from Nick Featherstone and Jean Louis Akpa Akpro.