Surfaces that exhibit contact angles close to 180° for both polar and non-polar solvents are rare. Here we report the fabrication of such “omniphobic” surfaces by photolithography. We investigate their stability against a so-called wetting transition during evaporation of millimetric water droplets by systematically varying the shape and surface roughness of the micropillars on the surface. We show that a low edge curvature of the top of the micropillars strongly delays the transition, while it completely disappears when the surface roughness is increased. We compare these experimental findings with existing models that describe the Cassie–Baxter to Wenzel transition and conclude that new models are needed which include the hurdle of an energy barrier for the wetting transition. Our results reveal that by increasing the roughness of the micropillars we do not affect the apparent equilibrium contact angle of the droplets. The dynamic robustness of the surface is, however, dramatically enhanced by an increase of the surface roughness.