Conventional microstrip patch antennas can be easily miniaturized by increasing the substrate electric permittivity (εr) although the fractional bandwith (FBW) is dramatically decreased. In this work, the use of metamaterials as artificial antenna substrates is studied as an alternative method to eficiently miniaturize patch antennas, accounting not only electric permittivity εr but also magnetic permeability μr. In addition, a compact FBW formulation proposed by Yaghjian et al. [10] is applied to compute the maximum achievable bandwidth of patch antennas with both homogeneous and dispersive material substrates. Several prototypes with artificial metasubstrates have been fabricated to assess the simulations results, leading to a proper patch antenna miniaturization while maintaining its FBW.