V6O11 and V7O13 are two members of the VnO2n−1 Magnéli series (n=3–9). At ambient pressure, V6O11 manifests a metal to insulator (MI) transition near TMI=170 K and V7O13 (the exception in the series that does not become insulating at ambient pressure) manifests an antiferromagnetic (AFM) transition with spin density wave character at TN=43 K. Temperature-dependent resistivity data for V6O11 and V7O13 were measured under pressures up to 7.52 and 6.40 GPa, respectively with critical pressures of PMIc=3.8 GPa for V6O11 and PAFMc=3.5 GPa for V7O13. As the MI transition for V6O11 is suppressed no features associated with an AFM transition in the resistivity are seen. Near the critical pressure for V6O11 where the first-order MI transition disappears, a T2 dependence of the low-temperature resistance can be found. On the other hand, in V7O13 as the second-order, antiferromagnetic transition is brought towards T=0, the resistivity shows a vanishing low-temperature region of Fermi-liquid-like behavior, consistent with proximity to a quantum critical point. Improved hydrostaticity of the pressurized sample space enhances the divergence of the T2 coefficient for V7O13 near the AFM critical pressure, 3.5 GPa.