Background Assessing fitness to drive and predicting driving cessation remains a challenge for primary care physicians using standard screening procedures. The objective of this study was to prospectively evaluate the properties of neuropsychological screening tests, including the Trail Making Test (TMT), Clock Drawing Test (CDT), Montreal Cognitive Assessment (MoCA), Useful Field of View (UFOV), and Timed Up and Go (TUG) test, in predicting driving cessation for health reasons in drivers older than 70 years of age. Design and methods This prospective cohort study, with a median follow-up of 4 years for drivers of 70 years old or older with an active driving license in Switzerland, included 441 participants from a driving refresher course dedicated to volunteer senior drivers. Cases were drivers reported in the national driving registry who lost their license following a health-related accident, who were reported as unfit to drive by their physician or voluntarily ceased driving for health reasons. Survival analysis was used to measure the hazard ratio of driving cessation by adjusting for age and sex and to evaluate the predictive value of combining 3 or more positive tests in predicting driving cessation during a 4-year follow-up. Results A total of 1738 person-years were followed-up in the cohort, with 19 (4.3%) having ceased driving for health reasons. We found that participants with a TMT-A < 54 sec and TMT-B < 150 sec at baseline had a significantly lower cumulative hazard of driving cessation in 4 years than those with slower performance (adjusted HR 3, 95% CI: 1.16–7.78, p = 0.023). Participants who performed a CDT ≥ 5 had a significantly lower cumulative hazard of driving cessation (adjusted HR 2.89, 95% CI: 1.01–7.71, p = 0.033). Similarly, an MoCA score ≥ 26, TUG test <12 sec or a UFOV of low risk showed a lower but not significant cumulative risk at a median follow-up of 4 years. When using tests as a battery, those with three or more positive tests out of five were 3.46 times more likely to cease driving (95% CI: 1.31–9.13, p = 0.012). Conclusions The CDT and the TMT may predict driving cessation in a statistically significant way, with a better performance than the UFOV and MoCA tests during a median 4-year follow-up. Combining tests may increase the predictability of driving cessation. Although our results are consistent with current evidence, they should be interpreted with precaution; more than 95% of the participants above the set threshold were able to continue driving for 4 years without any serious incident.