Wednesday only had two shots, which were off-target, in the 90 minutes as Michael Mifsud was denied on a couple of occasions in the second half.
Coventry did manage a shot on goal when Kevin Thornton's header released Leon Best and his right-wing cross dropped to Jay Tabb. He controlled the ball before firing in a close-range shot which Lee Grant smothered.
Referee Jarnail Singh was the busiest man in the first half as he booked Elliott Ward for an early challenge on Richard Hinds, before then showing yellow cards to Franck Songo'o, Grant and Tommy Spurr in a ten-minute spell as the game threatened to spill over.
Wednesday didn't force their first corner until the 39th minute which Graham Kavanagh took and when the ball eventually came back into the box, Richard Wood failed to properly connect and Kasper Schmeichel was able to grab possession.
Coventry finally began to put the Owls' defence under some concerted pressure.
Mifsud exchanged passes with Tabb, but instead of electing to pass to Michael Doyle on the edge of the six-yard box, the Malta international elected to shoot and hit the sidenetting.
In the next attack, Mifsud teed up Doyle with a right-wing centre, but the Irishman's header hit right-back Hinds and flew over the bar.
Doyle was substituted after appearing to take a knock to the head in the challenge.
The Sky Blues should have broken the deadlock in the 68th minute when Tabb's great pass picked out the run of Thornton, but the midfielder fired his shot wide of the far post.
Danny Fox's fantastic 40-yard pass sent Mifsud clear and his shot was tipped wide by Grant.
Mifsud had another chance when Isaac Osbourne knocked the ball back to him and he unleashed an 18-yard shot which was deflected wide.