The peculiar sphenoidal “pits” of the common warthog (Phacochoerus africanus) long have been recognized as a feature that distinguishes that species from the closely related desert warthog (P. aethiopicus). Authors seem to regard these structures as blind pockets that do not extend beyond the basicranium. However, these structures actually are openings that lead into a complex system of sinuses (the sphenoidal sinuses) located in the sphenoid and squamosal, and occasionally extending into the occipital and parietal bones. The openings appear to serve as a drain into the nasopharynx. The sphenoidal “pits” of P. africanus as currently defined by most authors are, therefore, not homologous with the sphenoidal pits of P. aethiopicus. We suggest that the term “sphenoidal apertures” be applied to these openings. The true homologue of the sphenoidal pits of P. aethiopicus is the bone that surrounds the sphenoidal apertures in P. africanus. This would include the thin bony sheet that forms the floor of the opening and that bears a shallow fossa. We recommend the term “sphenoidal shelf” be employed to describe this part of the true sphenoidal pit of P. africanus. In addition to the sphenoidal sinuses, the maxillary and frontal sinuses of P. africanus also are described. We report the possibility of mammalian cranial sinuses arising from nasopharyngeal diverticula rather than from diverticula originating from the nasal cavity proper. Previously, such nasopharyngeal pneumatization only has been known to occur in Reptilia. Possible sinus functions are discussed including shock absorption, lightening of the skull, improvement of olfaction, and enhancement of the immune system. In addition to P. africanus, sphenoidal apertures also occur in Babyrousa, and in an extinct perissodactyl, a brontothere (= titanothere).