Summary To establish a dose–response relationship between the strength of electromagnetic fields (EMF) and previously reported effects on the brain, we investigated the influence of EMF exposure by varying the signal intensity in three experimental sessions. The head of 15 healthy male subjects was unilaterally exposed for 30 min prior to sleep to a pulse‐modulated EMF (GSM handset like signal) with a 10 g‐averaged peak spatial specific absorption rate of (1) 0.2 W kg –1 , (2) 5 W kg –1 , or (3) sham exposed in a double‐blind, crossover design. During exposure, subjects performed two series of three computerized cognitive tasks, each presented in a fixed order [simple reaction time task, two‐choice reaction time task (CRT), 1‐, 2‐, 3‐back task]. Immediately after exposure, night‐time sleep was polysomnographically recorded for 8 h. Sleep architecture was not affected by EMF exposure. Analysis of the sleep electroencephalogram (EEG) revealed a dose‐dependent increase of power in the spindle frequency range in non‐REM sleep. Reaction speed decelerated with increasing field intensity in the 1‐back task, while accuracy in the CRT and N‐back task were not affected in a dose‐dependent manner. In summary, this study reveals first indications of a dose–response relationship between EMF field intensity and its effects on brain physiology as demonstrated by changes in the sleep EEG and in cognitive performance.