The system comprises firstly an electronic label and, secondly, a label reader. The label comprises a foil made of a material that conducts magnetic fields and has a low coercive field. It is placed against the antenna and is parallel to the antenna to form a shield and a flux concentrator for the electromagnetic waves. The reader comprises bars surrounded by coils to generate a magnetic field so that the lines of said magnetic field can get looped in passing into the label when the reader is placed in the vicinity of this label. If the object on which the label is placed is provided with a protective cup, the invention provides for positioning plates, made of a material similar to that of the foil, between the bars and the protective cup. Application to the remote identification of objects, in particular metal objects such as gas cylinders.