Nice thread here!
This year, obviously, it's my year to learn more about swarming. If I want to make sure that I got the queen in the swarm that I gathered, I like this method so far:
Building upward - bottom board, q excluder, medium, q excluder, medium, lid. This way I can dump the swarm into the top medium, put the lid on, wait a couple of hours or so. When the bees go thru the q excluder I can spot the queen... or not. Because it's a swarm and the bees are in swarm mode, I like to keep them nestled in this set up for 24 hrs-ish. I also add a frame of brood to the bottom box and incentive for the bees to go below.
With this last swarm, I saw and captured the queen. I put her into the bucket with the rest. Later in the evening, we lightly sprayed sugar syrup on the bees and piece by piece drew out all the debri that came with the swarm. I'll be goll darned is we could not find the queen. Hence, my question of if she could have gone thru the q excluder.