Background The proportion of SARS-CoV-2 positive persons who are asymptomatic—and whether this proportion is age-dependent—are still open research questions. Because an unknown proportion of reported symptoms among SARS-CoV-2 positives will be attributable to another infection or affliction, the observed , or 'crude' proportion without symptoms may underestimate the proportion of persons without symptoms that are caused by SARS-CoV-2 infection. Methods Based on two rounds of a large population-based serological study comprising test results on seropositivity and self-reported symptom history conducted in April/May and June/July 2020 in the Netherlands ( n  = 7517), we estimated the proportion of reported symptoms among those persons infected with SARS-CoV-2 that is attributable to this infection, where the set of relevant symptoms fulfills the ECDC case definition of COVID-19, using inferential methods for the attributable risk (AR). Generalised additive regression modelling was used to estimate the age-dependent relative risk (RR) of reported symptoms, and the AR and asymptomatic proportion (AP) were calculated from the fitted RR. Results Using age-aggregated data, the 'crude' AP was 37% but the model-estimated AP was 65% (95% CI 63–68%). The estimated AP varied with age, from 74% (95% CI 65–90%) for < 20 years, to 61% (95% CI 57–65%) for the 50–59 years age-group. Conclusion Whereas the 'crude' AP represents a lower bound for the proportion of persons infected with SARS-CoV-2 without COVID-19 symptoms, the AP as estimated via an attributable risk approach represents an upper bound. Age-specific AP estimates can inform the implementation of public health actions such as targetted virological testing and therefore enhance containment strategies.