I only know of one conference where this is done, the Gordon Bell Prize, and the Best Paper and Best Student Paper prizes. The are all judged, unblinded, after all the candidate talks have been presented at the Supercomputing conference because the quality of each talk plays into the jurors' opinions about the work. The papers themselves are examined first, double-blind by completely different review panels earlier in the year in order to decide whether to accept them to the confernce or not.
For conference papers, this makes a lot of sense because the talk is a part of the criteria for the award. I ignored your suggestion about the timing of the award, because this is the only case I know of that both reviews the paper and gives a prize. If you're interested in a case where the talk is irrelevant, please update your question with specifics.