We present experimental results on the giant magnetoresistance effect in magnetic multilayers measured with the current perpendicular to the multilayer plane. Two different experimental techniques are used, which both allow the study of the perpendicular magnetoresistance from 4 to 300 K. The first technique is based on the fabrication of pillar-like microstructures of Fe/Cr and Co/Cu multilayers using microlithography and reactive ion etching. In the second technique we use holographic laser interference nanofabrication and wet anisotropic etching to pattern V-shaped grooves of 0.2 µm width into semi-insulating InP substrates. Subsequently, a Co/Cu multilayer is evaporated at an angle with the substrate normal, naturally resulting in a perpendicular magnetoresistance configuration. Both experimental techniques demonstrate that the perpendicular magnetoresistance is a factor 2 to 4 larger than the conventional current-in-plane magnetoresistance.