Cognitive deficits are common following stroke and have many negative consequences. They must be identified to provide appropriate interventions and care. In Denmark, the Montreal Cognitive Assessment (MoCA), a dementia screening tool, is commonly used to screen for cognitive deficits following stroke, despite its limitations in this context. This study aimed to make the Oxford Cognitive Screen (OCS), a stroke-specific cognitive screening tool, available in Danish and to provide population appropriate normative data. Additionally, the study aimed to evaluate the appropriateness of the MoCA cutoff of 25/26 currently used in Denmark. A sample of healthy Danish participants aged 36–89 was assessed using the Danish OCS and MoCA. Mean performance and 5th percentile cutoffs were calculated for both tests. OCS results were similar to results from European studies. For the MoCA, 5th percentile corresponded to 22.35, suggesting that the cutoff currently used in Denmark is inappropriate.