Swindon, who have not drawn 0-0 for over a year, failed to find the target without leading scorer Sam Parkin and have now not won in their last seven games.
The home side made most of the running early on and had chances to open the scoring, but couldn't find the killer touch in the final third.
On three minutes, midfielder Matt Hewlett's right wing cross found veteran striker Tommy Mooney in the box, only for his bullet header to come crashing back off the left hand post.
The home side again hit the woodwork on 11 minutes when David Duke's 25 yard curling effort this time came back off the crossbar.
On 15 minutes, Mooney was again in the thick of the action when his headed centre to Junior Lewis saw the on loan midfielder put the ball into the back of the net only for it to be ruled out by an offside flag.
The visitors posed little threat in an attacking sense and their only real chance of the first half came on 32 minutes when striker Adrian Littlejohn inswinging free kick from the right fizzed past the far post as defender Sam Collins just failed to connect.
In a somewhat similar second half, chances were again limited, but the visitors almost claimed a shock lead on 77 minutes when tricky striker Stephen McPhee wriggled past his marker.
Vale's top scorer turned inside the defender Nicholas but his angled volley was saved by Swindon goalkeeper Rhys Evans.
Swindon's only telling contribution of the second period came three minutes from time when sub John Stevenson out a header from a Brian Howard corner well wide to sum up the home side's afternoon.
Port Vale manager Brian Horton said; "It was a hard fought game and I'm pleased we've kept another clean sheet, but we never really got going in the final third." "It's a useful point away from home and it's one we can build on in the coming weeks."