Neutralizing antibodies (nAbs) hold promise as effective therapeutics against COVID-19. Here, we describe protein engineering and modular design principles that have led to the development of synthetic bivalent and tetravalent nAbs against SARS-CoV-2. The best nAb targets the host receptor binding site of the viral S-protein and its tetravalent versions can block entry with a potency that exceeds the bivalent nAbs by an order of magnitude. Structural studies show that both the bivalent and tetravalent nAbs can make multivalent interactions with a single S-protein trimer, observations consistent with the avidity and potency of these molecules. Significantly, we show that the tetravalent nAbs show much increased tolerance to potential virus escape mutants. Bivalent and tetravalent nAbs can be produced at large-scale and are as stable and specific as approved antibody drugs. Our results provide a general framework for developing potent antiviral therapies against COVID-19 and related viral threats, and our strategy can be readily applied to any antibody drug currently in development.