The numerical investigation of quenching distances in laminar flows is mainly concerned with two setups: head-on quenching (HOQ) and side-wall quenching (SWQ). While most of the numerical work has been conducted for HOQ with good agreement between simulation and experiment, far less analysis has been done for SWQ. Most of the SWQ simulations used simplified diffusion models or reduced chemistry and achieved reasonable agreement with experiments. However, it has been found that quenching distances for the SWQ setup differ from experimental results if detailed diffusion models and chemical reaction mechanisms are employed. Side-wall quenching is investigated numerically in this work with steady-state 2D and 3D simulations of an experimental flame setup. The simulations fully resolve the flame and employ detailed reaction mechanisms as well as molecular diffusion models. The goal is to provide data for the sensitivity of numerical quenching distances to different parameters. Quenching distances are determined based on different markers: chemiluminescent species, temperature and OH iso-surface. The quenching distances and heat fluxes at the cold wall from simulations and measurements agree well qualitatively. ... mehrHowever, quenching distances from the simulations are lower than those from the experiments by a constant factor, which is the same for both methane and propane flames and also for a wide range of equivalence ratios and different markers. A systematic study of different influencing factors is performed: Changing the reaction mechanism in the simulation has little impact on the quenching distance, which has been tested with over 20 different reaction mechanisms. Detailed diffusion models like the mixture-averaged diffusion model and multi-component diffusion model with and without Soret effect yield the same quenching distances. By assuming a unity Lewis number, however, quenching distances increase significantly and have better agreement with measurements. This was validated by two different numerical codes (OpenFOAM and FASTEST) and also by 1D head-on quenching simulations (HOQ). Superimposing a fluctuation on the inlet velocity in the simulation also increases the quenching distance on average compared to the reference steady-state case. The inlet velocity profile, temperature boundary condition of the rod and radiation have a negligible effect. Finally, three dimensional simulations are necessary in order to obtain the correct velocity field in the SWQ computations. This however has only a negligible effect on quenching distances.