Thanks for the comments, guys!
I water them by flooding the large UV-resistant plastic tray underneath. My large tray holds 12 of those big square pots, the smaller one fits 8. I got them from a dog kennel supplier.
When I go on vacation, they go wanting! I can ignore these guys for over a week and they do fine. The nice thing about net pots for Neps is that you can leave them in an inch or two of water for a while without the plants noticing. I actually kept the largest two there, my sanguinea and alata x ventrata, in standing water for almost all of last winter - I think the trays went dry two or three times over four or five months.
They're aquatic plant pots, and I got them at Lowes'/Ace. Sometimes they have them, sometimes they don't, I just buy a half a dozen whenever I see some and can afford them.
And finally, no, it's a frog humidifier, and his name is Gero-gero-kun. (From Target, before you ask.)
~Joe