The FIRST virgin emerges and starts her mating flights. She is going to REPLACE the old queen.
She wont mate until they have found a permanent home in a different location. its not the queen that wants to swarm, its the bees. The bees stop feeding the queen so she can fly, they are the ones who make that decision, so doing in a queen, removing a queen etc.. changes nothing about what the bees want. Thats why they will swarm with the first Virgin, and why it is so difficult to convince them NOT to swarm once they have decided they were going to.
Removing the old queen and a few frames worth of bees is usually enough to convince the remaining bees that they swarmed, and they will return to work as usual.. Leaving enough bees to produce a good honey crop.
Now, waiting a few days, or even a couple weeks and returning the swarm to the hive via a newspaper combine, without the old queen may work.. but by then I have usually gotten the artificial swarm well started in a hive or nuc of their own.