I know this could generate a lot of opinions - here's mine.
Whether swarm or supercedure, I think the bees know best what to do - mind you, they are working ONLY with the situation at hand. Since over-crowded conditions (or a rise in hive temp is present) venting often helps - that could be in the way of tilting the outer cover, but ideally adding a screened bottom board.
The best single method to help keep the bees in that hive is to add a super with drawn comb. That isn't easy because most of us don't keep drawn foundation around, we put them back in the hive ASAP in most cases, so the second thing to do is to add a super with foundation frames and feed the bees sugar water to help the quickly produce a massive amount of wax. The availability of space and the means to create wax are a great combo to aid them in staying where they are.
If you are sure that the queen is alive and well - you could destroy the new cells, or if your queen is older and needs replacing - you may concidar removing her (not killing her yet) and let a new queens hatch from the queen cells and the workers will readily accept the new queen. If you were to do this, it's better to do it sooner than later - having a missing queen while the queens are being raised will help end the swarm mode.
The point: try making the hive less swarm worthy. Having more space, cooler temperatures and a need for a queen (with queen cells already present) are all good ways to keep the girls at home. It's always better to keep them there compared to trying to capture them later.
The alternative is to move the frame(s) with queen cells into another hive body with frames with foundation and feed that hive until it establishes itself with enough cells to both house food and brood.
Hope these have helped. I think an idea number of days when trying the first methods above is about five days prior to hatching. By removing the existing queen, her scent will dissipate just as the new queens emerge.
Of course, you could also kill the old queen, but I think that it is best to keep her in a nuc or other hive with a frame full of food, brood and workers UNTIL you see that the new queen cells are NOT duds. Nothing worse than killing of an old queen just to find your new queens never emerge.