Efficient, wide-scale testing for SARS-CoV-2 is crucial for monitoring the incidence of the infection in the community. The gold standard for COVID-19 diagnosis is the molecular analysis of epithelial secretions from the upper respiratory system captured by nasopharyngeal (NP) or oropharyngeal swabs. Given the ease of collection, saliva has been proposed as a possible substitute to support testing at the population level. Here, we used a novel saliva collection device designed to favour the safe and correct acquisition of the sample, as well as the processivity of the downstream molecular analysis. We tested 1003 nasopharyngeal swabs and paired saliva samples self-collected by individuals recruited at a public drive-through testing facility. An overall moderate concordance (68%) between the two tests was found, with evidence that neither system can diagnose the infection in 100% of the cases. While the two methods performed equally well in symptomatic individuals, their discordance was mainly restricted to samples from convalescent subjects. The saliva test was at least as effective as NP swabs in asymptomatic individuals recruited for contact tracing. Our study describes a testing strategy of self-collected saliva samples, which is reliable for wide-scale COVID-19 screening in the community and is particularly effective for contact tracing.