We have developed a new micro-fabricated platform for the measurement of the specific heat of low heat capacity mg-sized metallic samples, such as superconductors, down to temperatures of as low as 10 mK. It addresses challenging aspects of setups of this kind such as the thermal contact between the sample and platform, the thermometer resolution, and an addenda heat capacity exceeding that of the samples of interest (typically nJ/K at 20 mK). The setup allows us to use the relaxation method, where the thermal relaxation following a well defined heat pulse is monitored to extract the specific heat. The sample platform (5 × 5 mm2) includes a micro-structured paramagnetic Ag:Er temperature sensor, which is read out by a dc-superconducting quantum interference device via a superconducting flux transformer. In this way, a relative temperature precision of 30nK/\sqrt{Hz} can be reached, while the addenda heat capacity falls well below 0.5 nJ/K for T < 300 mK. A gold-coated mounting area (4.4 × 3 mm2) is included to improve the thermal contact between the sample and platform.