Bulls boss Jamie Pitman, who saw his side go down 6-1 at home to Gillingham last weekend, will have finished the happier manager as the visitors absorbed considerable second-half pressure to claim a deserved away point - ending a run of three successive defeats.
Cheltenham went closest to forcing a goal in a low-key first half when Hereford skipper Stefan Stam cleared Darryl Duffy's 10th-minute scrambled effort off the line following a Marlon Pack corner.
Sam Winnall's strong run produced the visitors' best chance, but after beating two defenders his angled shot drifted harmlessly wide.
The hosts seized control after the break and a sweeping move ended with Stam making his second last-ditch clearance of the day, this time to deny Josh Low's angled volley.
Hereford's on-loan Swansea keeper David Cornell then produced a diving fingertip save to push the outstanding Pack's cross-shot to safety, before Low missed a glaring chance to open the scoring - the midfielder unable to convert Jimmy Spencer's throughball when one-on one with the Bulls keeper.
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