Micromegas detectors, thanks to their good spatial and temporal discrimination capabilities, are good candidates for rare event search experiments. Recent X-ray background levels achieved by these detectors in the CAST experiment have motivated further studies in the nature of the background levels measured. In particular, different shielding configurations have been tested at the Canfranc Underground Laboratory, using a microbulk type detector which was previously running at the CAST experiment. The first results underground show that this technology, which is made of low radiative materials, is able to reach background levels down to 2 × 10-7 keV-1 s-1 cm-2 with a proper shielding. Moreover, the experimental background measurements are complemented with Geant4 simulations which allow to understand the origin of the background, and to optimize future shielding set-ups.