The quenching of premixed laminar flames at various constant pressures was studied through numerical simulation, with the Trajectory Generated Lower Dimensional Manifold (TGLDM) method used to employ detailed chemical mechanisms for stoichiometric methane and heptane flames. The method was validated at lower pressures and wall temperatures. The laminar flame speed predicted by the TGLDM method agrees reasonably well with experimental data reported in the literature. The peak heat flux at quenching was found to be under-predicted by 30-40% of the most current experimental data.The quench distance was calculated for pressures of 1, 2, 20 and 40 bar, with wall temperatures of 300 and 600 K and fresh gas temperature of 300 K. The quench distance was found to decrease with increasing pressure in a manner similar to previous studies. The value of quench distance for heptane was found to be smaller than that of methane by a factor of ~30% over all pressures.The peak heat flux values were used to evaluate the thermal model of Boust et al., for calculating quench distance and was found to predict the right trend, though the quench distance values are lower than those observed in experiment. The applicability of these results to internal combustion engines is briefly discussed by calculating a rough estimate of the fuel left unburned in the quenching layer for a spark-ignited engine, and a proposal for the computational implementation of Boust's thermal model is explained.