I hived 5 swarms out of 4 hives this spring. 2 of the swarms proved sterile and are now dwindling. My assessment after the "leave them alone for a few weeks" stage is that a queen introduction and/or a frame of young eggs do not represent a successful salvage strategy.
Does the 3 out of 5 swarm success percentage sound low or is this about what a field run rate would be/
However in the future I am considering adding a frame of eggs immediately after the swarm hives to every swarm, as this would shorten the queen raise/mate/egg laying period sufficiently that a sterile swarm might still establish. Has anyone manipulated their swarms this way? Do keeping the eggs covered in a swarm nuc take labor and care away from a fertile queen in sufficient numbers to be counterproductive.
On a related question, I have had two mother hives (one this year, and one last) go sterile and dwindle after releasing a swarm. I lost both these swarms so I not sure of the queen status of the released swarms. Do beeks manage the "mother" hive to make sure the remaining bees have a fertile queen, add a frame of eggs as above for the new swarm?
As long as I have the resources and if it doesn't hurt the contributing hive I like to give a newly hived swarm a frame of eggs. I believe that it helps anchor the swarm and in case of a queen problem the bees will decide what to do. I started doing this when I didn't have a lot of time to do inspections and it seems to work.
To answer another of your questions on the mother hive after a swarm, yes you should moniter it to see if there is a laying queen and if not a frame of eggs would be in order.
This is how I would manage them. Others might have different opinions but this has worked for me.