I always set my old queen aside in a small nuc with just a couple of frames of brood and maybe some sealed honey. That way, if your bees don't end up with a laying queen for whatever reason, you can always re-introduce her, or you can keep putting a frame with her eggs in another hive so they can try again.
Years ago, I had only one hive and hadn't been paying enough attention to it. I finally got into it and found it full of bees, with lots of nectar in the brood nest, no open brood, and queen cells all over. I knew they'd probably swarm no matter what I did, but I decided to split them anyway. So, I split the hive as evenly as I could, brood, queen cells, honey, and put a new deep with empty comb and foundation on top of each. After a few of days of rain, nothing had happened and I thought I was good, then on the next nice day, my kids told me that both hives had swarmed. Inside both, there were not near as many bees and none of the queens looked like they had hatched yet. I thought, "oh well, I won't get any honey, but at least I'll have two decent colonies with young queens. Then after a couple more days, they both swarmed again. I got into them and in one of them I saw a virgin queen crawling around on a comb, piping loudly. It was the first time I'd heard that and it was pretty cool. I found one of the after-swarms in a bush nearby, and I just collected them in a box and took the cover off one of the hives, pulled out a couple of the frames and dumped them all in. The next day there was a dead queen in front of that hive.