While it is quite easy to reliably produce queen bees by splitting hives, it is very wasteful of resources.
It is much better to use a dedicated cell building hives to produce individual cells that can be used to make 2 frame nucs.
Grafting is the technique used by large commercial queen breeders, but many small producers find the level of skill required to successfully graft impractical.
There are a number of cell plug devices such as Jenter, Cupkit, Cupularvae etc.
I am using the Jenter purely because I used it quite successfully 15 years ago. All these systems are essentially the same, having a plastic comb matrix with a queen excluder over the top.
The back of the device has removable plastic plugs containing the egg, larva which is transferred into the cell builder hive after the egg has hatched on the 4th day from being laid. It is important to get the youngest larvae possible.
The queen is confined in the Jenter kit for 24 hours, then released and the frame inserted in the middle of the brood nest for 3 days, on day 4, the plugs are removed and larvae inserted in the holders pictured. This is inserted into the cell builder hive
2 days after this, it will be obvious whether cells have been accepted or not.
All being well, on the 11th or 12th day these cells can then be inserted into a 2 frame nuc with a frame of honey and pollen and a frame with some open brood- push the cell carefully into the midst of the open brood facing the honey frame and reduce the entrance.
By day 15-16 queens will have emerged, but need several days to harden up to be able to fly and mate.
By day 30, eggs and larvae should be visible, if no eggs by day 37, it did not work out and you will need to destroy the queen and give another cell or reunite the nuc with a production colony.
The crucial element to success with this is to use a good Cell builder hive. There are a wide variety of techniques using starter / finisher hives in a variety of configurations.
I tried several times to use a queenless starter and queenright finisher without success.
As soon as I put the started cells in the queenright finisher the bees would tear them down.
After a lot of research I came across some notes from Michael Bush regarding the use of a queenless starter / finisher and this has worked well for me.
This technique uses only 6 frames, so is quite conservative and efficient use of bees.
Place 2 frames of honey and pollen on the outside edges of your hive. next put a frame of open brood adjacent to one of the pollen frames- then your empty Cell carrier frame, 2 frames of sealed brood and a feeder. Push these frames together.
Now shake 3 frames of nurse bees from 3 separate hives into the box, and close up.
Remove your strongest hive from it’s stand, and place this cell builder hive in it’s place and open to a medium entrance reducer.
You will now have a box absolutely packed with bees in a queenless state.
They will build queen cells on the frame of open brood, and get them primed for your real target cell building on the jenter plugs. They will be extremely annoyed and likely to sting pretty ferociously.
The reason for using so few frames is to simulate overcrowded conditions that cause bees to swarm, so you will be activating both swarm and emergency impulses for cell building.
On the day after you make up this box, confine your queen mother in the jenter kit in the middle of her brood nest.
On the next day, liberate your queen back into her hive and replace the jenter kit with the eggs facing a frame of open brood.
On the 4th day after the queen is liberated from the jenter kit, remove the frame of brood from your cell builder – it will be covered in capped and nearly capped queen cells,. You can use this frame as is to start a 2 frame nuc, or wait until day 12 and cut out suitable cells to make up nucs from this frame. The sealed queens are fragile at this time so do not shake or invert this frame.
Now you should check your cell builder for any other queen cells on the sealed brood frames and destroy them, so that your target jenter cells are not destroyed by an early hatching queen.
Make up your cell bar with about 15 cells- from the jenter plugs. don’t use more as you are aiming for quality. Insert the queen cell bar where the frame of open brood was.
These larvae will now be the ONLY larvae of suitable age and will be readily accepted.
After 5 days they will be sealed, and you can start another cell bar of cells at this time if wanted.
On day 12 they can come out for distribution to nucs.
You can keep this cell builder hive going indefinitely by adding a frame or 2 of sealed brood every week to 10 days. inspect for rogue queen cells on the sealed brood frames every 3 days. One virgin queen will destroy your efforts and end the usefulness of this cell builder hive.
If this is all the cells you need, just leave one ripe cell behind in the cell builder and it will become a strong nuc, keep an eye on it for the next few weeks, as the bees may be in the mood to swarm and build queen cells from the first lot of eggs laid by the new queen.
Michael Bush has great information and you will probably find his writing a lot less confusing than mine!