Late yesterday, I had the new (to me) experience of watching a new queen emerge from her cell. Fortunately, I had taken the camera out with me and was able to capture it for other folks to see.
How it came about: I was dealing with a swarm and checking a hive for queen cells, only to find a queen cell, just opened, and the new queen emerging. It took almost 25 minutes for the queen and the workers that figured out what was happening to get the hole opened widely enough for her to get out. Then yours truly, while attempting to bet the worker bees out and keep the queen in the cup so I could mark her, allowed the queen to scurry off into the hive. I did a check for her, but by the time all this finished, my smoker was out and it was dusk. I had to end the hunt as the girls were getting a bit peevish.
Lesson learned: just capture them all, and then go about dealing with getting the workers out of the cup so the queen can be marked.