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Danny was next to threaten for the visitors, but after exchanging passes with Ronaldo his strike from the edge of the box was hit straight at the keeper.
Portugal continued to pose the greater threat and Ronaldo fired a shot just wide of the far post after charging through the midfield.
Ronaldo was seeing plenty of the ball for his country and following another powerful run, his cross to the near post was headed narrowly over the bar by Nani.
Against the run of play Denmark came close to taking the lead when Michael Krohn-Dehli curled a low strike from just inside the box onto the far post.
Lasse Vibe had another chance for the hosts just before the break, but his flicked effort did not have enough power to beat the keeper.