Serological SARS-CoV-2 assays are needed to support clinical diagnosis and epidemiological investigations. Recently, assays for the large-volume detection of total antibodies (Ab) and immunoglobulin (Ig) G and M against SARS-CoV-2 antigens have been developed, but there are limited data on the diagnostic accuracy of these assays. This study was organized as a Danish national collaboration and included fifteen commercial and one in-house anti-SARS-CoV-2 assays in sixteen laboratories. Sensitivity was evaluated using 150 serum samples from individuals diagnosed with asymptomatic, mild or moderate nonhospitalized (n=129) or hospitalized (n=31) COVID-19, confirmed by nucleic acid amplification tests, collected 13-73 days from symptom onset. Specificity and cross-reactivity were evaluated in samples collected prior to the SARS-CoV-2 epidemic from > 586 blood donors and patients with autoimmune diseases or CMV or EBV infections. Predefined specificity criteria of ≥99% were met by all total-Ab and IgG assays except one (Diasorin/LiaisonXL-IgG 97.2%). The sensitivities in descending order were: Wantai/ELISA total-Ab (96.7%), CUH/NOVO in-house ELISA total-Ab (96.0%), Ortho/Vitros total-Ab (95.3%), YHLO/iFlash-IgG (94.0%), Ortho/Vitros-IgG (93.3%), Siemens/Atellica total-Ab (93.2%), Roche-Elecsys total-Ab (92.7%), Abbott-Architect-IgG (90.0%), Abbott/Alinity-IgG (median 88.0%), Diasorin/LiaisonXL-IgG (84.6%), Siemens/Vista total-Ab (81.0%), Euroimmun/ELISA-IgG (78.0%), and Snibe/Maglumi-IgG (median 78.0%). The IgM results were variable, but one assay (Wantai/ELISA-IgM) had both high sensitivity (82.7%) and specificity (99%). The rate of seropositivity increased with time from symptom onset and symptom severity. In conclusion, predefined sensitivity and specificity acceptance criteria of 90%/99%, respectively, for diagnostic use were met in five of six total-Ab and three of seven IgG assays.