Conventional approaches to isolate and characterize nanobodies are laborious. We combine phage display, multivariate enrichment, next-generation sequencing, and a streamlined screening strategy to identify numerous anti-severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) nanobodies. We characterize their potency and specificity using neutralization assays and hydrogen/deuterium exchange mass spectrometry (HDX-MS). The most potent nanobodies bind to the receptor binding motif of the receptor binding domain (RBD), and we identify two exceptionally potent members of this category (with monomeric half-maximal inhibitory concentrations around 13 and 16 ng/ml). Other nanobodies bind to a more conserved epitope on the side of the RBD and are able to potently neutralize the SARS-CoV-2 founder virus (42 ng/ml), the Beta variant (B.1.351/501Y.V2) (35 ng/ml), and also cross-neutralize the more distantly related SARS-CoV-1 (0.46 μg/ml). The approach presented here is well suited for the screening of phage libraries to identify functional nanobodies for various biomedical and biochemical applications.