For centuries, paleontologists have sought functional explanations for the uniquely complex internal walls (septa) of ammonoids, extinct shelled cephalopods. Ammonoid septa developed increasingly complex fractal margins, unlike any modern shell morphologies, throughout more than 300 million years of evolution. Some have suggested these morphologies provided increased resistance to shell-crushing predators. We perform the first physical compression experiments on model ammonoid septa using controlled, theoretical morphologies generated by computer-aided design and 3D printing. These biomechanical experiments reveal that increasing complexity of septal margins does not increase compression resistance. Our results raise the question of whether the evolution of septal shape may be tied closely to the placement of the siphuncle foramen (anatomic septal hole). Our tests demonstrate weakness in the centers of uniformly thick septa, supporting work suggesting reinforcement by shell thickening at the center of septa. These experiments highlight the importance of 3D reconstruction using idealized theoretical morphologies that permit the testing of long-held hypotheses of functional evolutionary drivers by recreating extinct morphologies once rendered physically untestable by the fossil record.