The exchange bias properties of nanopatterned thin films of Co, on top of which a native Co-oxide layer develops spontaneously, are studied by means of magnetic and magneto-resistance measurements. Both continuous and patterned films are investigated, the latter in the form of antidot arrays prepared with the self-assembling polystyrene nanospheres technique. The obtained antidot arrays are in the hexagonal close-packed configuration and cover a surface area of several square millimetres. Nanopatterned samples turn out to have a very good repeatability of their magnetic and magneto-resistive properties. The presence of a native oxide is responsible for the development of an exchange bias effect at temperatures below ~150 K, which has been reported both on hysteresis loops and on magneto-resistance curves; these consist of a superposition of an anisotropic magneto resistance (AMR) effect and a giant magneto-resistance (GMR)-like effect. The determination of the bias field by means of the two different sets of data is consistent and gives a complete picture of the phenomenology in this kind of nanopatterned magnetic systems