Update on the way out? ie. Pop up with two options "close" and "update and close", at least this time you've already accomplished what you were after with the application.
Especially one that will relaunch the app when it's done.
Ideally, you'd want a system-level daemon that downloads and preps updates in the background, and either waits until the system is idle (I think Apple has some tech like this already for running Time Machine backups), with pending updates optionally installed on system shutdown (am I shutting down to save on battery, to restart, or because I'm about to leave the office and I don't care how long it takes for the system to shut down).
I think Kelly Sutton (of the late layervault) figured this out with his fork of sparkle, called "autosparkle" - https://github.com/layervault/Sparkle . I haven't personally integrated it into my app yet, but supposedly it makes updates a much more silent process - which is really important for 'always-on' tray apps like layervault was, or the one I'm making.
What I've always wanted, and no one seems to do, is to have the update box pop up on startup (as usual), and then have a button that says "Install on quit." Then I wouldn't have to be interrupted when I opened an app to do something, and it would be taken care of when I finished so that it's ready for the next time.