A numerical study on a high-pressure laminar counterflow diffusion flame is presented. Extinction limits are studied at pressures up to 100 atm for two cases: one with pure methane and the other for a diluted mixture of methane with 40% water vapor mass fraction. The fuel stream flows against pure oxygen on both cases. Solutions for the 1D ideal-gas model and for a real-gas model are provided with both detailed and reduced chemical kinetics, and are compared against real-gas results from the literature. Previous studies increased the strain rate by rising the inflowing velocities of the opposing streams, yielding very high speeds near extinction. Here, strain rate is increased mainly by moving the nozzles closer to each other and also by small increases in the inflow velocities until extinction occurs. When no water is present, there is good agreement in the extinction strain rate between all the cases. However, substantial differences appear in extinction temperature, which features a local minimum between 70 atm and 90 atm, which was not previously reported in the literature. Furthermore, when water vapor is mixed with the fuel, both extinction strain rate and extinction temperature behave differently with increasing pressure. Extinction strain rate increases with pressure and reaches an asymptotic value at about 50 atm, while extinction flame temperature increases from 1 atm to 20 atm, and then decreases almost linearly.