The next few days I watched three swarms depart from another hive as I hadn't removed surplus Queen cells.
During my first year looking after bees (I can't call myself a bee keeper) a similar thing happened, and I overzealously removed all the Queen cells, leaving my hive Queen-less.
The "extra" queen cells can be "harvested" and used to stop or delay swarming in the colony they are produced in and distributed to splits (divided colonies) of other colonies to increase colony numbers.
The beekeeper doesn't do anything except check the colony for swarm preparation-meaning queen cells.
It's predictable and successful in obtaining queen cells
Cell builder: Honey bees will want to raise a queen(s) when queenless, and accept prepared larvae to start queen cells.
Approximately nine days later queen cells created along the edge that you trimmed will be ready to harvest by gently cutting them intact from the frame and using them to requeen queenless hives or place in nuc boxes to use later.
The best side of the comb is used for the queen cells and is prepared by destroying two rows of worker cells and leaving one, beginning at the top of the frame.
Some kind of support is necessary to hold the comb far enough above the frame to leave plenty of room for drawing large queen cells.
If the above instructions are followed, a large amount of queen cells can be produced as simply and easily as any method that I have seen or tried.