New signing Cedric van der Gun made his home debut, while there was a welcome return on the bench for Ferrie Bodde
After early sparring from both sides, Joe Allen raced clear down the middle in the seventh minute but, with only the keeper to beat, he lifted his shot high and wide.
The Robins almost opened the scoring in the 11th minute when a corner by Paul Hartley was headed down by Liam Fontaine but Dorus de Vries saved with his legs.
The Swans were caught on the break midway through the half when Evander Sno raced down the left and cut inside but his shot went across the goal and behind to safety.
A neat move down the left involving Andrea Orlandi put the visitors defence under pressure but Nathan Dyer over-ran the ball and the chance was lost.
In the 33rd minute, the busy Dyer fired in a shot on the run that whistled just wide of the far post.
Four minutes later, van der Gun struck an upright with a header from an Orlandi corner.
The half drew to a close with both sides passing the ball around midfield but with very little goalmouth action.
The Swans started the second half with a little more urgency and penned the Robins back on defence without troubling the recalled Adriano Basso in the visitors goal.
When Orlandi headed a Jordi Lopez corner down and inside the near post on the hour, Basso dived across to scramble clear.
Craig Beattie replaced Gorka Pintado up front for the Swans in the 65th minute and there were the loudest cheers of the night when Bodde went on for Orlandi four minutes later.
Beattie had a glorious chance after Allen worked him through but he shot tamely at Basso and then the goal opened up for Bodde five minutes from time but he dithered over the ball and the Robins cleared their lines.
The Swans had several chances to snatch victory in the closing minutes but a point apiece was a fair return for two poor performances.