The local heat-release rate and the thermo-chemical state of laminar methane and dimethyl ether flames in a side-wall quenching configuration are analyzed. Both, detailed chemistry simulations and reduced chemistry manifolds, namely Flamelet-Generated Manifolds (FGM), Quenching Flamelet-generated Manifolds (QFM) and Reaction-Diffusion Manifolds (REDIM), are compared to experimental data of local heat-release rate imaging of the lab-scale side-wall quenching burner at Technical University of Darmstadt. To enable a direct comparison between the measurements and the numerical simulations, the measurement signals are computed in all numerical approaches. Considering experimental uncertainties, the detailed chemistry simulations show a reasonable agreement with the experimental heat-release rate. The comparison of the FGM, QFM and REDIM with the detailed simulations shows the high prediction quality of the chemistry manifolds. For the first time, the thermo-chemical state during quenching of a dimethyl ether-air flame is examined numerically. Therefore, the carbon monoxide and temperature predictions are analyzed in the vicinity of the wall. The obtained results are consistent with previous studies for methane- air flames and extend these findings to more complex oxygenated fuels. Furthermore, this work presents the first comparison of the QFM and the REDIM in a side-wall quenching burner