The measuring system includes a receiver including at least one fixed receiving antenna for picking up electromagnetic fields generated by a transmitting antenna belonging to an electronic device, and a positioning device on which a support element is placed. The positioning device includes mechanisms for driving the support element in rotation. The measuring system further includes a detection device for detecting position/orientation of the transmitting antenna, and a data processing station. A hollow spherical element houses the electronic device, and is held on the positioning device by gravity on three points, one of which is formed by a drive member, and the two other points are formed using ball and socket joints. Several circular barcodes arranged on the external surface of the spherical element enable the system to determine the position/orientation of the spherical element using the digital camera.