This study aimed to investigate the relationship between pre-pandemic objective and subjective cognitive functioning and sustained Internet use during the pandemic among older adults in Switzerland. Data from 1299 respondents of the Survey of Health, Ageing and Retirement in Europe (SHARE) in 2019/2020 and a supplementary technology use questionnaire during the pandemic in 2021 were used. Cognitive functioning was assessed in 2019/2020 through objective measures (delayed and immediate memory, verbal fluency) and self-rated memory. Sustained Internet use was defined as having used the Internet at least once in the past seven days in 2019/2020 and reporting daily or weekly use in 2021. We found that 73.1% of respondents consistently used Internet between 2019/2020 and 2021. Using multivariable probit regression models controlling for sociodemographic and health variables, we found that higher global cognition z-scores, especially in immediate and delayed memory, were associated with a higher likelihood of sustained Internet use. Additionally, respondents with good, very good, or excellent self-rated memory were more likely to sustain their Internet use. These findings highlight the potential critical role of cognitive health in shaping older adults' digital engagement, suggesting that cognitive assessments and training should be further considered in digital literacy initiatives for this population.