As a guild leader, it is almost certain that you have those one or two people that you rely on to help get stuff done. Maybe they’re a healing lead or main tank. Perhaps they’re an officer, or class leader, or even just a close friend who is a member. You’ve probably said something like, “Man, if you quit I’d just shut down the guild.” Ha ha ha! Let’s test that!
One way or the other, if you’re running a guild for any length of time it’s likely that you’ll have to learn to operate without that person. As of yesterday I am in this extremely unfortunate position myself, so I offer the following advice from experience.
1) Don’t Panic! Resist the temptation to run to guild site and post, “Oh god, X has quit WoW. What are we going to do?! We’re SCREWED.” Guilds can be pretty sensitive places when a beloved core member quits, and the members will be looking to you for reassurance that everything will be okay. Give them some.
2) Don’t be afraid to show your emotions in a calm manner. If you’re sad, it’s okay to share that in the appropriate places. That sadness is actually a bonding experience for everyone involved, and you need a little solace too.
3) Remain focused and present. Try and gently express that while everyone is sad now (and you are too), the show is going on. And even though you might want to hide under your bed for a week.. don’t! Log on and stand around the Auction House if nothing else. People will feel better if you and other officers are present and available to talk.
4) Don’t immediately try and replace the departed. Really, they are probably irreplaceable. Instead wait a few weeks and see how the guild organically works things out.
Essentially, don’t try and pretend that you are a robot with no emotions, but on the other hand let people know that the guild is still stable and life will go on. And, most times, it will. It still sucks though. Sigh.

I miss the restaurant but not the waiting on the tables.
The restaurant misses you, too.