In the present paper, we propose a new theoretical approach to evaluate the shape and apparent contact angle (ACA) of a drop gently deposited on microstructured superhydrophobic surfaces. We exploit the very large separation of scales between the drop size and the features of the micromorphology of the interface to propose a numerical methodology to calculate the apparent contact area and apparent contact angle. In agreement with very recent experiments, calculations show that, in the case of surfaces made of conical micropillars, the ACA may take values very close to 180° not depending on the size of the liquid drop. At large drop volumes, the shape of the drop deviates from the spherical one as a result of the gravity effects, but it is noteworthy that the apparent contact angle does not change at all. Our calculations shows that this holds true also for different pillar shapes, showing that, for any given Young contact angle of the solid constituting the pillars, the ACA is an intrinsic property of the surface microgeometry.