Tranmere came closest when they hit the bar just after half time.
Swindon's best chance came after 78 minutes when Danny Invincibile went round the Tranmere keeper, but the angle was too great and he missed the open goal.
Both keepers did have a few saves to make, but overall a draw was a fair result, and leaves Swindon 15th, subject to Bury staying in the league, which if Bury do fold beofre the end of the season will see Swindon lose 6 points.