The position of an object, for example a catheter, in a body to be examined is determined so as to enable monitoring of its movement through the body at the same time that information concerning the anatomy in the surroundings of the object is to be acquired. An as high as possible temporal and spatial resolution should be achieved for this purpose. To this end, the nuclear magnetization in the surrounding region of the object is determined by means of a micro-coil which is mounted on the inserted object, it being possible to determine the position of the object from the nuclear magnetization. Subsequently, an RF coil system is used to perform a line scan around this position in order to determine the nuclear magnetization in a line-shaped region.