This work presents an evolutionary approach to pinna design. Narrowband echolocating bats move the pinna to alter the directional sensitivity of their perceptual systems. Adding pinnae to RoBat—a biomimetic sonarhead mounted on a mobile robot—is the goal of this work. After a description of the earlier work on artificial pinnae consisting of multiple reflectors around the transducer, an acoustic model, inspired by a physical model of sound diffraction and reflections in the human concha, is described and revisited as the model to use for evolving complex shapes. A genetic algorithm evolved the shape of the pinnae with respect to desired features of the directivity pattern of the receiver transducers. Some interesting paraboloid shapes for specific echolocating behaviors were evolved, improving performance with respect to the bare transducer's performance.