Serological testing for SARS-CoV-2-specific antibodies provides important research and diagnostic information relating to COVID-19 prevalence, incidence and host immune response. A greater understanding of the relationship between functionally neutralising antibodies detected using microneutralisation assays and binding antibodies detected using scalable enzyme immunoassays (EIA) is needed in order to address protective immunity post-infection or vaccination, and assess EIA suitability as a surrogate test for screening of convalescent plasma donors. We assessed whether neutralising antibody titres correlated with signal cut-off ratios in five commercially available EIAs, and one in-house assay based on expressed spike protein targets. Sera from recovered patients or convalescent plasma donors who reported laboratory-confirmed SARS-CoV-2 infection (n = 200), and negative control sera collected prior to the COVID-19 pandemic (n = 100), were assessed in parallel. Performance was assessed by calculating EIA sensitivity and specificity with reference to microneutralisation. Neutralising antibodies were detected in 166 (83%) samples. Compared with this, the most sensitive EIAs were the Cobas Elecsys Anti-SARS-CoV-2 (98%) and Vitros Immunodiagnostic Anti-SARS-CoV-2 (100%), which detect total antibody targeting the N and S1 antigens, respectively. The assay with the best quantitative relationship with microneutralisation was the Euroimmun IgG. These results suggest the marker used (total Ab vs. IgG vs. IgA) and the target antigen are important determinants of assay performance. The strong correlation between microneutralisation and some commercially available assays demonstrates their potential for clinical and research use in assessing protection following infection or vaccination, and use as a surrogate test to assess donor suitability for convalescent plasma donation.