Conventional approaches to isolate and characterize nanobodies are laborious and cumbersome. Here we combine phage display, multivariate enrichment, and novel sequence analysis techniques to annotate an entire nanobody repertoire from an immunized alpaca. We combine this approach with a streamlined screening strategy to identify numerous anti-SARS-CoV-2 nanobodies, and use neutralization assays and Hydrogen/Deuterium exchange coupled to mass spectrometry (HDX-MS) epitope mapping to characterize their potency and specificity. Epitope mapping revealed that the binding site is a key determinant of neutralization potency, rather than affinity alone. The most potent nanobodies bind to the receptor binding motif of the RBD, directly preventing interaction with the host cell receptor ACE2, and we identify two exceptionally potent members of this category (with monomeric IC50s 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.