Rapid testing for Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2) of patients presenting to emergency departments (EDs) facilitates the decision for isolation on admission to hospital wards. Differences in the sensitivity of molecular assays have implications for diagnostic workflows. This study evaluated the performance of the cobas® Liat® RT-PCR, which is routinely used as the initial test for ED patients in our hospitals, compared with the eazyplex® RT-LAMP. A total of 378 oropharyngeal and nasal swabs with positive Liat® results were analysed. Residual sample aliquots were tested using NeuMoDx™, cobas® RT-PCR, and the eazyplex® assay. Patients were divided into asymptomatic (n = 157) and symptomatic (n = 221) groups according to the WHO case definition. Overall, 14% of positive Liat® results were not confirmed by RT-PCR. These samples were mainly attributed to 26.8% of asymptomatic patients, compared to 3.8% of the symptomatic group. Therefore, positive Liat® results were used to provisionally isolate patients in the ED until RT-PCR results were available. The eazyplex® assay identified 62% and 90.6% of RT-PCR-confirmed cases in asymptomatic and symptomatic patients, respectively. False-negative eazyplex® results were associated with RT-PCR Ct values > 30, and were more frequent in the asymptomatic group than in the symptomatic group (38.1% vs. 5.1%, respectively). Both the Liat® and eazyplex® assays are suitable for testing symptomatic patients. Their use in screening asymptomatic patients depends on the need to exclude any infection or identify those at high risk of transmission.