To control the rise in Neisseria meningitidis strain W infections, during 2018–2019, the Netherlands launched a catch-up meningococcal conjugate (MenACWY) vaccination campaign for teenagers (13–18 years of age). Applying a mental models approach, we surveyed teenagers and their parents about their knowledge and beliefs about meningococcal disease, the MenACWY vaccination, vaccinations in general, and their MenACWY vaccination intentions. Using random forest analysis, we studied predictions of vaccination intentions by knowledge and beliefs. Survey response rate was 52.8% among teenagers and 59.4% among parents. MenACWY vaccination intentions were best predicted by knowledge and beliefs about vaccinations in general, surpassing knowledge and beliefs about meningococcal disease and the MenACWY vaccination. For teenagers, their parents’ intention that the teenager be vaccinated was a strong predictor of the teenagers’ own vaccination intention. To optimize vaccination uptake during future outbreaks, we recommend that communications emphasize the effectiveness and safety of vaccines and continue to focus on parents.