Molecular junctions offer significant potential for enhancing thermoelectric power generation. Quantum interference effects and associated sharp features in electron transmission are expected to enable the tuning and enhancement of thermoelectric properties in molecular junctions. To systematically explore the effect of quantum interferences, we designed and synthesized two new classes of porphyrins, P1 and P2, with two methylthio anchoring groups in the 2,13- and 2,12-positions, respectively, and their Zn complexes, Zn-P1 and Zn-P2. Past theory suggests that P1 and Zn-P1 feature destructive quantum interference in single-molecule junctions with gold electrodes and may thus show high thermopower, while P2 and Zn-P2 do not. Our detailed experimental single-molecule break-junction studies of conductance and thermopower, the latter being the first ever performed on porphyrin molecular junctions, revealed that the electrical conductance of the P1 and Zn-P1 junctions is relatively close, and the same holds for P2 and Zn-P2, while there is a 6 times reduction in the electrical conductance between P1 and P2 type junctions. Further, we observed that the thermopower of P1 junctions is slightly larger than for P2 junctions, while Zn-P1 junctions show the largest thermopower and Zn-P2 junctions show the lowest. We relate the experimental results to quantum transport theory using first-principles approaches. While the conductance of P1 and Zn-P1 junctions is robustly predicted to be larger than those of P2 and Zn-P2, computed thermopowers depend sensitively on the level of theory and the single-molecule junction geometry. However, the predicted large difference in conductance and thermopower values between Zn-P1 and Zn-P2 derivatives, suggested in previous model calculations, is not supported by our experimental and theoretical findings.