The formation and progression of in-stent restenosis (ISR) in bifurcated vessels may vary depending on the technique used for stenting. This study evaluates the effect of a variety of mesh styles on the accuracy and reliability of computational fluid dynamics (CFD) models in predicting these regions, using an idealized stented nonbifurcated model. The wall shear stress (WSS) and the near-stent recirculating vortices are used as determinants. The meshes comprise unstructured tetrahedral and polyhedral elements. The effects of local refinement, as well as higher-order elements such as prismatic inflation layers and internal hexahedral core, have also been examined. The uncertainty associated with individual mesh style was assessed through verification of calculations using the grid convergence index (GCI) method. The results obtained show that the only condition which allows the reliable comparison of uncertainty estimation between different meshing styles is that the monotonic convergence of grid solutions is in the asymptotic range. Comparisons show the superiority of a flow-adaptive polyhedral mesh over the commonly used adaptive and nonadaptive tetrahedral meshes in terms of resolving the near-stent flow features, GCI value, and prediction of WSS. More accurate estimation of hemodynamic factors was obtained using higher-order elements, such as hexahedral or prismatic grids. Incorporating these higher-order elements, however, was shown to introduce some degrees of numerical diffusion at the transitional area between the two meshes, not necessarily translating into high GCI value. Our data also confirmed the key role of local refinement in improving the performance and accuracy of nonadaptive mesh in predicting flow parameters in models of stented artery. The results of this study can provide a guideline for modeling biofluid domain in complex bifurcated arteries stented in regards to various stenting techniques.