This is simple and gives good queens, when 10-20 queens is needed at once. If more than 20 queens is needed use Brother Adams method (same as Michael Palmer).
Simple no extra gear queen rearing system which can be used all summer in the same colony.
1. Divide a very strong two story colony, which has brood in both boxes
2. Find the queen and put her with the frame she is walking in the upper box. Destroy all queen cells.
3. Shake nurse bees from 4 frames of open brood to the lower box.
4. In the lower box remove one frame (capped extra food for instance), put frame of young larvae in the middle and a frame with lots of stored pollen (bee bread) beside the young larvae frame. Place the emptly gap between those two.
5. Put a plastic sheet on top of the lower box
6. Put a ½ inch stick of wood on the plastic sheet, near the rear of the lower box, this stick provides a rear entrance to the upper box, close other entrances in the upper box.
7. Close the hive for at least 4 hours, more if the weather is bad
8. Do the grafting and put the frame of grafted larvae in the gap in the lower box
9. Wait 24 hours
10. Remove the plastic sheet and wooden stick. Place a queen excluder between the boxes.
11. Wait 4 days (5 days from the start) queencells are capped and it is good practise to protect them if you have gear for that. If not wait 9 days for the cells to be ripe and use them in any queenless hive by putting them between the frames.