On‐call work is used to manage around the clock working requirements in a variety of industries. Often, tasks that must be performed while on‐call are highly important, difficult and/or stressful by nature and, as such, may impact the level of anxiety that is experienced by on‐call workers. Heightened anxiety is associated with poor sleep, which affects next‐day cognitive performance. Twenty‐four male participants (20–35 years old) spent an adaptation, a control and two counterbalanced on‐call nights in a time‐isolated sleep laboratory. On one of the on‐call nights they were told that they would be required to do a speech upon waking (high‐stress condition), whereas on the other night they were instructed that they would be required to read to themselves (low‐stress condition). Pre‐bed anxiety was measured by the State Trait Anxiety Inventory form x‐1, and polysomnography and quantitative electroencephalogram analyses were used to investigate sleep. Performance was assessed across each day using the 10‐min psychomotor vigilance task (09:30 hours, 12:00 hours, 14:30 hours, 17:00 hours). The results indicated that participants experienced no significant changes in pre‐bed anxiety or sleep between conditions. However, performance on the psychomotor vigilance task was best in the high‐stress condition, possibly as a result of heightened physiological arousal caused by performing the stressful task that morning. This suggests that performing a high‐stress task may be protective of cognitive performance to some degree when sleep is not disrupted.