The Madison airport isn't a great place to eat, but the Wurst Bar, featuring Usinger's sausages, is probably your best bet -- any of the wursts or the Reuben are fine, as long as you don't mind eating something heavy before your flight. Certainly beats the subpar airport version of the Great Dane, a packaged sandwich from Ancora, or the unspeakable Quizno's, your other options here.
(The best option, if you've got time, is to stop at Smoky Jon's on the way to the airport and get takeout.)