I like to try to get as even a split as possible and this is the way I do it.
I always wait till I see swarm cells but you can do this beforehand as a sort of pre-emptive swarm control.
I move the parent box at least 3 metres away. In the place of the original colony I put a brood box of drawn comb (you can have half drawn half foundation if you are short). I take out a frame with open brood and shake the bees off it; make sure there are NO QUEEN CELLS. I put this into the middle of the new brood box and put the supers back on top. This box has all the flying bees but no queen so they will make emergency queen cells. It will become the artificial swarm.
Back at the parent box on a new site I put the one spare frame at the edge. This box has the queen, all the queen cells and NO flying bees. They will tear down all their queen cells.
If they have few stores you can feed a little but foragers are made every day and will soon be out and about.
9/10 days later (but absolutely no later than 12) I go back to the parent colony, find the queen and just pop her back onto the top bars of the Artificial Swarm. There is no need to cage her. She is the bees’ old queen and they will accept her straight away. You must break down ALL the emergency queen cells they have made. The queen has lots of foragers and all the young bees in the supers so she will romp away.
Back at the parent box having removed the queen they will make emergency cells. They have lots of nurse bees and the ability to make a good queen. There is no need to thin these cells down. The bees have no intention of swarming and will do the job themselves. They will build up quickly too and you should get a good crop of both splits if the weather is good