Opened up hive today, didn't find a queen, and no sight of any eggs. Yikes!!!

In a hive that JUST swarmed, there is often no sign of fresh eggs - the queen stopped laying a few days before to get ready for her flight with the swarm. However there should be capped brood and probably several swarm cells (queen larvae)near the bottom of the brood box. Easiest way to tell is to CAREFULLY tip up the whole box with the most capped brood, and look for peanut shaped protrusions hanging down or between frames. If any of these is sealed (no small smooth hole near the bottom), you already have a queen in the oven, who should emerge in a few days. Hives rarely swarm without leaving a new queen "in the works." Wait a couple weeks and check for brand new eggs again.

Good advice above. I'll add that if your not sure what you're looking at, close them up and walk away for about three weeks and then check again. Most of the time they'l have a new queen and if they don't it will be obvious then and you can deal with it.
When they swarm like that, watch the swarm. Alot of times they land fairly close by and they are really easy to catch. Then you have a new hive and if the old one comes up queenless you can combine the two back together.