Both sides passed the ball well and created plenty of chances without being able to take them so both sets off supporters left Whaddon Road frustrated.
Cheltenham dominated possession and had the lion's share of chances but Walsall were always dangerous on the break and could easily have taken all three points had they capitalised on the few good opportunities they created.
Cheltenham controlled the first half and should have been ahead at the break, although it was the visitors who hit the woodwork twice during the opening 45 minutes.
Walsall goalkeeper Clayton Ince was a busy man in the early stages, getting down sharply to save a powerful shot from Josh Payne and then flying to his left to push aside a long-range strike from Lee Ridley.
Ince then reacted quickly to push aside a shot from Barry Hayles as Cheltenham threatened to take the lead, although they did prove vulnerable to the quick counter-attack.
Michael Ricketts almost opened the scoring midway through the first half with a shot that clipped the crossbar and striker Troy Deeney hit the base of a post shortly afterwards when Alex Nicholls had sent him clear with an intelligent pass.
It was the same story after the break and, although young on-loan midfielder Payne had the ball in the net for Cheltenham, he was flagged offside.
Home goalkeeper Scott Brown made good saves from both Alex Nicholls and Deeney, while defender Andy Gallinagh cleared a header from Ricketts off the line.
It was one of those afternoons when neither side looked like scoring even if they played until next Christmas, although this had a lot more to do with good defensive organisation than poor attacking play.
Cheltenham remain in the bottom three but will draw plenty of encouragement from this performance. Walsall, meanwhile, continue to look like a team in the process of rebuilding under manager Jimmy Mullen.