The Robins controlled the game after the first 20 minutes but just could not get the vital goal and Lincoln after a lively start were left desperately hanging on for a point.
City created the first chance of the game on 17 minutes when Gary Taylor-Fletcher crossed from the left. Jamie McCombe climbed highest in the box but his header was pushed over by Cheltenham keeper Shane Higgs.
Then Simon Yeo forced his way through from his own half but his attempt to find Taylor-Fletcher came to nothing.
Cheltenham had a great chance to break the deadlock in the 23rd minute. Striker Steve Guinan was left for a free header from 10 yards and saw his effort saved by Lincoln keeper Alan Marriott.
On the half-hour Ashley Vincent caught out the Lincoln defence with an excellent cross from the left but Brian Wilson shot wide from six yards.
Cheltenham's John Finnigan then won a challenge on the edge of the box and set up Vincent.
The teenager sent in a low shot which Marriot did well to keep out. Lincoln escaped in the 67th minute when defender Paul Morgan appeared to handle but referee Grant Hegley ignored penalty claims.
Moments later Vincent was put clear but his powerful shot was well saved by Marriot.
Lincoln managed a rare attack in the 74th minute when substitute Francis Green broke clear but put his shot went wide.
Lincoln were then reduced to bombing high balls into the Cheltenham area which was easily dealt with by the Robins defence.
Cheltenham had a late chance to take all three points when they won a free-kick just outside the box.
Former West Ham player Grant McCann hit an excellent shot over the defensive wall but Marriot saved to earn the Imps a home point.