I do not like them to sit wet either.
I either run the sterilizer right before I will be using the nebs and take them out as soon as the cycle is done (they shake off nearly dry if you take them out right away), or airdry them on a wire baking rack (the kind with little legs, so air circulates around them.)
The Germ Guardian uses dry heat and is marketed to sanitize DRY baby toys, pacifiers, etc. Instructions for it state that it's not meant to be used with wet things, and I am leery about using a product like that in a way it's not intended. Since it doesn't reach a temperature sufficient to sterilize, I am not convinced the interior is germ-free, so i don't want to put freshly sterilized nebs into a container that may not be sterile and leave them in there for prolonged periods of time. However, that's just my opinion. Some people love theirs. <img src="i/expressions/face-icon-small-smile.gif" border="0">