Finding the queen and caging her are not steps that are included in my swarm collections. Take an empty deep (brood chamber) and scoop the bees in or whatever maneuver best collects the balled bees. Have never lost a queen. Most of the time I even skip the cardboard box.
My grandfather-in-law was the first to truck hives to Florida for the orange crop, back in the 1920s. He was quite the bee entrepreneur - queen breeding, honey sales, etc.
His day job was Methodist minister, which in those days didn't pay particularly well. He also was a U.S. Marshal in Arizona Territory back when things were still pretty wild and wooly out there.