The conformations of five doubly neo-confused porphyrin structures and fifty-four neo-confused N-confused porphyrin (neo-C-NCP) tautomers were minimized using DFT-B3LYP/6-311++G(d,p). The relative stabilities of the tautomers for each series were computed using M06-2X and B3LYP-D functionals, and the bond lengths and bond angles were calculated. Nucleus-independent chemical shifts and anisotropy of induced current density plots were used to provide further insights into the diatropic properties of each species. The results demonstrate that porphyrinoid structures with two modified rings of this type are far less stable than porphyrins, N-confused porphyrins, or neo-confused porphyrins, but the fully conjugated tautomers retain highly diatropic characteristics. Nevertheless, the lowest-energy neo-C-NCP tautomers have similar relative energies to known doubly N-confused porphyrins, and the results suggest that these types of porphyrin isomers may be synthetically accessible.