Objectives Cognitive screening is recommended in stroke, but test completion may be complicated by stroke related impairments. We described feasibility of completion of three commonly used cognitive screening tools and the effect on scoring properties when cognitive testing was entirely/partially incomplete. Methods We performed a cross‐sectional study, recruiting sequential stroke patient admissions from two University Hospital stroke rehabilitation services. We assessed Folstein's mini‐mental state examination (MMSE), Montreal cognitive assessment (MoCA) and Addenbrooke's cognitive examination (ACE‐III). The multidisciplinary team gave an independent diagnostic formulation. We recorded numbers fully/partially completing tests, assistance and time required for testing. We calculated test discrimination metrics in relation to clinical assessment using four differing statistical approaches to account for incomplete testing. Results We recruited 51 patients. Direct assistance to complete cognitive tests was required for 33 (63%). At traditional cut‐offs, the majority screened “positive” for cognitive impairment (ACE‐III: 98%; MoCA: 98%; MMSE: 81%). Comparing against a clinical diagnosis, ACE‐III and MoCA had excellent sensitivity but poor specificity. Partial completion of cognitive tests was common (ACE‐III: 14/51, MMSE: 22/51; MoCA: 20/51 fully complete); greatest non completion was for test items that required copying or drawing. Adapting analyses to account for these missing data gave differing results; MMSE sensitivity ranged from 0.66 to 0.85, and specificity ranged from 0.44 to 0.71 depending on the approach employed. Conclusions For cognitive screening in stroke, even relatively brief tools are associated with substantial incompletion. The way these missing data are accounted for in analyses impacts on apparent test properties. When choosing a cognitive screening tool, feasibility should be considered and approaches to handling missing data made explicit. Copyright © 2016 John Wiley & Sons, Ltd.