In order to obtain new materials for energy storage as supercapacitors, Cobalt–Nitrogen doped mesoporous carbons were prepared from pyrolysis of two Cobalt Metal-Organic Frameworks (MOFs), one linear coordination polymer and one complex (not polymeric). The material derived from Cobalt 2,3-pyrazinedicarboxylate polymer (700 °C) exhibited a specific capacitance of 330 F g^-1 (after acid leaching, in 6 M KOH, 1 A g^-1). This material exhibited a reduction in its capacitance of only 2% after 3000 charge-discharge cycles. A specific capacitance of 430 F g^-1 was reached after the addition of ferrocianide to the electrolyte. A correlation was found between the specific capacitance and both the specific surface area of mesopores and the Cobalt content. This correlation allowed discriminating between the pseudocapacitance and the double layer contributions to the total specific capacitance. Finally, a prototype symmetric capacitor was constructed which yielded a specific energy of 9.1 W h kg^-1 (0.1 A g^-1) and a specific power of 7 kW kg^-1 (10 A g^-1). A device constructed with two of these capacitors in series allowed to light a 1.5 V red LED.