Estimates of seroprevalence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) antibodies have been hampered by inadequate assay sensitivity and specificity. Using an enzyme-linked immunosorbent assay-based approach that combines data about immunoglobulin G responses to both the nucleocapsid and spike receptor binding domain antigens, we show that excellent sensitivity and specificity can be achieved. We used this assay to assess the frequency of virus-specific antibodies in a cohort of elective surgery patients in Australia and estimated seroprevalence in Australia to be 0.28% (95% Confidence Interval, 0-1.15%). These data confirm the low level of transmission of SARS-CoV-2 in Australia before July 2020 and validate the specificity of our assay.