Hi John,
I split a hive and took the old queen out when I saw some quite advanced queen cells in the hive.
The reason I took the queen is that they were looking like they were going to swarm anyway, and she would be attempting to leave. So it was better that I helped the colony satisfy the swarming desire. The queen and the rest of the hive "assumed" they had swarmed. The bees and the old queen settled straight down and are almost out to 6 frames now.
In the old hive I removed all but one of the cells. Again to stop them throwing casts. I checked yesterday and found and huge new queen running round in the hive.
Had I removed the frames with cells, there was no guarentee that the colony with the old queen would not have stopped trying to swarm.
I am sure others will offer other opinions, but this method works for me.