In this paper, the quenching of a laminar premixed flame at a cold inert wall is investigated. Transient system behavior of the quenching flame is studied both by using well known and widely used reaction mechanisms. Reduced models are developed for each particular mechanism. The different detailed mechanisms are applied and reduced by implementing a manifold-based approach - the REDIM method. The flame quenching is studied by using numerical simulations and by comparing different reaction mechanisms as well as different transport models and their corresponding reduced models. It is demonstrated that the results obtained by the detailed and reduced mechanisms differs much less than the results for different detailed mechanisms. This confirms the quality of the reduced model and verifies the reduced method developed by the REDIM approach.