Aims:The knowledge of the properties of the youngest radio sources is very important in order to trace the earliest phase of the evolution of the radio emission. RXJ1459+3337, with its high turnover frequency (~25 GHz) provides a unique opportunity to study this class of extreme objects. Methods: High-sensitivity multi-frequency VLA observations have been carried out to measure the flux-density with high accuracy, while multi-frequency VLBA observations were performed, aimed at determining the pc-scale structure. Archival ROSAT data have been used to infer the X-ray luminosity. Results: The comparison between our new VLA data and those available in the literature shows a steady increment of the flux-density in the optically-thick part of the spectrum and a decrement of the turnover frequency. In the optically-thin regime, the source flux density has already started to decrease. Such a variability can be explained in terms of an adiabatically-expanding homogeneous radio component. The frequency range spanned by our VLBA observations, together with the resolution achieved, allows us to determine the source size and the turnover frequency, and then to derive the magnetic field directly from these observable quantities. The value obtained in this way is in good agreement with that computed assuming equipartition condition. A similar value is also obtained by comparing the radio and X-ray luminosities.