Porphyrin-like metal-functionalized graphene structures have been investigated as possible catalysts for CO2 and CO reduction to methane or methanol. The late transition metals (Cu, Ag, Au, Ni, Pd, Pt, Co, Rh, Ir, Fe, Ru, Os) and some p (B, Al, Ga) and s (Mg) metals comprised the center of the porphyrin ring. A clear difference in catalytic properties compared to extended metal surfaces was observed owing to a different electronic nature of the active site. The preference to bind hydrogen, however, becomes a major obstacle in the reaction path. A possible solution to this problem is to reduce CO instead of CO2. Volcano plots were constructed on the basis of scaling relations of reaction intermediates, and from these plots the reaction steps with the highest overpotentials were deduced. The Rh–porphyrin-like functionalized graphene was identified as the most active catalyst for producing methanol from CO, featuring an overpotential of 0.22 V. Additionally, we have also examined the hydrogen evolution and oxidation reaction, and in their case, too, Rh–porphyrin turned out to be the best catalyst with an overpotential of 0.15 V.