Many migrating animals, belonging to different taxa, annually move across the globe and cover hundreds and thousands of kilometres. Many of them are able to show site fidelity, i.e. to return to relatively small migratory targets, from distant areas located beyond the possible range of direct sensory perception. One widely debated possibility of how they do it is the use of a magnetic map, based on the dependence of parameters of the geomagnetic field (total field intensity and inclination) on geographical coordinates. We analysed temporal fluctuations of the geomagnetic field intensity as recorded by three geomagnetic observatories located in Europe within the route of many avian migrants, to study the highest theoretically possible spatial resolution of the putative map. If migratory birds measure total field intensity perfectly and take the time of day into account, in northern Europe 81% of them may return to a strip of land of 43 km in width along one of coordinates, whereas in more southern areas such a strip may be narrower than 10 km. However, if measurements are performed with an error of 0.1%, the strip width is increased by approximately 40 km, so that in spring migrating birds are able to return to within 90 km of their intended goal. In this case, migrating birds would probably need another navigation system, e.g. an olfactory map, intermediate between the large-scale geomagnetic map and the local landscape cues, to locate their goal to within several kilometres.