I treat a new swarm like I would a package; feed them and leave them for 3 weeks (I don't even open the box except to add food). Cut outs, nucs are all treated the same as new packages. Patience is important; it is very easy for new keepers to want to see what is happening and opening the hive too often can result in slow-downs of hive production.
For established hives; I prefer a minimal approach. During primary swarm season I inspect weeks in order to asses population and crowding. At a minimum I lift each box and inspect the bottom of the frames to check for signs of swarm cells. Every 2 weeks I check for queenness (but only to the point of proving she is there and healthy, I don't need to see the queen to know if she is there and healthy).
What I do is my way but in the end you should establish what you want your way to be.
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