Frank Talia was called upon to make some rearguard action as Grant McCann, John Melligan and Brian Wilson all went close.
Jamie Victory struck the bar with a power header and Mike Williamson hoofed the ball off the line.
Wanderers boss John Gorman was happy to see half time and get the chance to revive his team.
In the second half Wanderers started well but again were pressed back by an adventurous Cheltenham.
Changes by Gorman saw new signing Sergio Torres replace Ian Stonebridge and Joe Burnell for veteran Rob Lee.
The impact was immediate as Torres beat two defenders to bring a fine save from Shane Higgs in the Town goal.
Danny Senda should have given Wycombe the lead on 62 minutes after some excellent inter-passing with Nathan Tyson, but his shot hit the side netting.
Stefan Oakes then brought another fine save from Higgs with a left foot sledgehammer on 66 minutes.
David Bird replaced Wilson and came close to a winner for Town on 88 minutes.
Michael Rose then brought a fine save from Talia as Wycombe held out for the final minutes under pressure.
In added on time both sides settled for the point.