ETA: Just discovered there was a Godzilla/Marvel (SHIELD) crossover. Ah, the internet.
Actually, the Marvel "Godzilla" comic series used SHIELD throughout its entire 24-issue run. 'Dum Dum' Dugan has the mission to follow and fight Godzilla. Later issues also had such guest stars as The Champions, Devil Dinosaur, the Fantastic Four and the Avengers. The series is collected in its entirety (though in b/w) in Marvel's "Essential Godzilla". I'd recommend it only for hardcore fans and nostalgics, though. Also, Marvel's Godzilla has a closer physical resemblance to the Hanna/Barbera cartoon version than to the Japanese original.