I split immediately I find a queen cell or a queen cup with royal jelly but I have a slightly different routine.
I place a new brood box on the original site with a mixture of drawn comb and foundation. I then place the queen and the frame she is on in the middle of this and add another frame of sealed brood and bees. I put on the queen excluder with supers above.
I then set the original colony on a new floor on top of the supers.
Any flying bees enter the bottom box on returning from foraging.
This has the effect of creating a strong honey producing colony on the original site with all the flyers, the bees in the supers, and very little brood. With the other part of the split, you have 8 days or more to decide what you want to do with it if none of the cells are sealed. If it a colony I want to rear queens from, I wait till a couple of days before emergence date and remove the cells with a scalpel to put in roller cages which can be wedged in a line between two frames which are seperated slightly. Alternately if there is a frame with just one cell you can take it out to put it straight into a nuc with a bit more brood and bees.
If the part of the split is one I don't want to breed queens from, I either requeen it with a queen cell from a better colony or split it up to make a series of nucs with other queen cells I have.
Another possibility at this stage is rejoining the two colonies if you don't want to make increase.
I learnt most of this from Finman's posts
and it has worked well for me this year as I have both strong honey producing colonies and about a dozen nucs.
The only swarm I lost this year is one which absconded from a nuc which I think overheated.
Just one proviso, this is not foolproof and you still have to do 8 day checks. Sometimes a colony is determined to swarm and will continue to make queen cells. In this case I do what crazy bull does and remove the queen to a nuc. It sure beats climbing ladders and scrambling through hedges after swarms.