Background The axial skeleton of extinct saurischian dinosaurs (i.e., theropods, sauropodomorphs), like living birds, was pneumatized by epithelial outpocketings of the respiratory system. Pneumatic signatures in the vertebral column of fossil saurischians include complex branching chambers within the bone (internal pneumaticity) and large chambers visible externally that are bounded by neural arch laminae (external pneumaticity). Although general aspects of internal pneumaticity are synapomorphic for saurischian subgroups, the individual internal pneumatic spaces cannot be homologized across species or even along the vertebral column, due to their variability and absence of topographical landmarks. External pneumatic structures, in contrast, are defined by ready topological landmarks (vertebral laminae), but no consistent nomenclatural system exists. This deficiency has fostered confusion and limited their use as character data in phylogenetic analysis. Methodology/Principal Findings We present a simple system for naming external neural arch fossae that parallels the one developed for the vertebral laminae that bound them. The nomenclatural system identifies fossae by pointing to reference landmarks (e.g., neural spine, centrum, costal articulations, zygapophyses). We standardize the naming process by creating tripartite names from “primary landmarks,” which form the zygodiapophyseal table, “secondary landmarks,” which orient with respect to that table, and “tertiary landmarks,” which further delineate a given fossa. Conclusions/Significance The proposed nomenclatural system for lamina-bounded fossae adds clarity to descriptions of complex vertebrae and allows these structures to be sourced as character data for phylogenetic analyses. These anatomical terms denote potentially homologous pneumatic structures within Saurischia, but they could be applied to any vertebrate with vertebral laminae that enclose spaces, regardless of their developmental origin or phylogenetic distribution.