Watson enters the office as Holmes goes through the files of recent deaths in the hospital, carrying two fresh cups of takeaway coffee. The following action reveals that the two actors were using empty cups.
Watson gives one of the cups to Holmes, who immediately drinks the coffee by tipping the cup past horizontal. If he had done this with a full cup of coffee, he would have ended up with a burnt face as the coffee escaped from the cups cap.
In the same scene, Watson takes the cap off her coffee, but none is visible in the cup, despite it being freshly purchased. When standing at the blackboard, she takes a sip from the cup, but judging by the possible coffee level from the earlier shot, she doesn't appear to tip the cup far enough to get anything out of it, had there been any in the cup .