County created the majority of the goalscoring opportunities and Glovers goalkeeper Chris Weale was particularly busy in the second half.
Stockport youngster Josh Thompson was unlucky as his 49th-minute header hit the crossbar but Ward was at least relieved to have gained a positive result after three straight defeats.
He said: "We had some good chances to score, but their keeper had a good game.
"Maybe we should have been a bit more clinical, but I suppose it was good for us to have secured a clean sheet.
"It would have been nice to have got the win, but getting a point at least stops the rot."
Source: Team_Talk