The visitors tested the opposition keeper early on when Steve Howard latched onto a cross, but his header was straight at Robert Olejnik.
Peterborough responded with a chance of their own, but Chris Kirkland made two fine stops in quick succession to deny the hosts before Miguel Llera scrambled the ball clear.
Wednesday almost broke the deadlock midway through the half when Giles Coke let fly from just outside the box, but his effort was well saved.
The Owls threatened again just a couple of minutes later when Peterborough's failure to clear the ball resulted in a goalmouth scramble, but the ball was eventually hacked to safety.
The visiting fans were celebrating just before half time when Anthony Gardner looked to have buried Danny Pugh's swinging corner, but it was the ball hitting the stanchion that caused the net to ripple.