The SARS coronavirus 2 (SARS-CoV-2) spike (S) protein binding to the human ACE2 receptor is the molecular event that initiates viral entry into host cells and leads to infection and virus replication. There is a need for agents blocking viral entry into host cells that are cross-reactive with emerging virus variants. VHH-72 is an anti-SARS-CoV-1 single-domain antibody that also exhibits cross-specificity with SARS-CoV-2 but with decreased binding affinity. Here we applied a structure-based approach to affinity-mature VHH-72 for the SARS-CoV-2 spike protein while retaining the original affinity for SARS-CoV-1. This was achieved by employing the computational platform ADAPT in a constrained dual-affinity optimization mode as a means of broadening specificity. Select mutants designed by ADAPT were formatted as fusions with a human IgG1-Fc fragment. These mutants demonstrated improved binding to the SARS-CoV-2 spike protein due to decreased dissociation rates. Functional testing for virus neutralization revealed improvements relative to the parental VHH72-Fc up to 10-fold using a SARS-CoV-2 pseudotyped lentivirus and 20-fold against the SARS-CoV-2 authentic live virus (Wuhan variant). Binding and neutralization improvements were maintained for some other SARS-CoV-2 variants currently in circulation. These improved VHH-72 mutants are predicted to establish novel interactions with the S antigen. They will be useful, alone or as fusions with other functional modules, in the global quest for treatments of COVID-19 infections.