Channel meandering is ubiquitous in tidal marshes, yet it is either omitted or weakly implemented in morphodynamic models. Here we propose a novel numerical method to simulate channel meandering in tidal marshes on a Cartesian grid. The method calculates a first-order flow by considering the balance between pressure gradient and bed friction. To account for flow momentum shift towards meander outer banks, the flow is empirically modified. Unlike previous simplified methods that relied on the curvature of the bank, this modification is based on the curvature of the flow, making the model suitable for use in dendritic channel networks. The modified flow intrinsically accounts for the topographic steering effect, which tends to deflect the momentum toward the outer bank. As a result, the outer bank becomes steeper and erodes due to soil creep. Additionally, the outer bank experiences erosion proportional to the flow curvature. This erosion mechanism parameterizes the direct erosion caused by flow impacting the bank through a proportionality coefficient, which modulates the rate of lateral channel migration. Deposition on the inner bank is automatically simulated by the model, triggered by reduced bed shear stress in that area. The model accurately reproduces channel lateral migration and sinuosity development, and associated processes such as meander cutoffs, channel piracies, and network reorganizations. The model provides an efficient tool for predicting marsh landscape evolution from decades to millennia, which will enable exploring how lateral migration and meandering of tidal channels affect marsh ecomorphodynamics, carbon and nutrient cycling, drainage efficiency, and pond dynamics.