Screening tests can be performed to identify stroke patients who require further assessment of swallowing function. The Repetitive Saliva Swallowing Test (RSST) is a screening test during which the patient is asked to swallow saliva as many times as possible for 30 s, while deglutition is counted through palpation of the larynx. This study aimed to establish normative values for three age groups of non-patients (total N = 120) on RSST. One patient group (N = 40) was also recruited from a geriatric stroke unit to assess whether RSST scores predicted outcomes on the Standardised Swallowing Assessment—Svenska (SSA-S), a clinical screening tool here used as a reference test. Since the RSST involves the swallowing of saliva, this study also measured the participants’ saliva secretion in order to examine its effect on RSST performance. This study showed that RSST results vary with age (lower among older) and gender (higher for men than women), while the number of doctor-prescribed medications, objective saliva secretion and self-assessed dryness of mouth did not affect the performance significantly. In comparison to a more extensive clinical screening procedure (SSA-S), the RSST correctly predicted 93% of negative cases and 69% of positive cases. This suggests that patients who show signs of aspiration according to SSA-S have a lower probability of detection with RSST.