Climate model components utilizing unstructured meshes enable variable resolution, regionally enhanced simulations within global domains. Here we investigate the relationship between mesh quality and simulation statistics using the JIGSAW unstructured meshing library and the Model for Prediction Across Scales‐Ocean (MPAS‐Ocean) with a focus on Gulf Stream dynamics. In the base configuration, the refined region employs 8 km cells that extend 400 km from the coast of North America. This coastal‐refined region is embedded within a low‐resolution global domain, with cell size varying latitudinally between 30 and 60 km. The resolution transition region between the refined region and background mesh is 600 km wide. Three sensitivity tests are conducted: (a) The quality of meshes is intentionally degraded so that horizontal cells are progressively more distorted; (b) the transition region from high to low resolution is steepened; and (c) resolution of the coastal refinement region is varied from 30 to 8 km. Overall, the ocean simulations are shown to be robust to mesh resolution and quality alterations. Meshes that are substantially degraded still produce realistic currents, with Southern Ocean transports within 0.4% and Gulf Stream transports within 12% of high‐quality mesh results. The narrowest transition case of 100 km did not produce any spurious effects. Refined regions with high‐resolution produce eddy kinetic energy and sea surface height variability that are similar to the high‐resolution reference simulation. These results provide heuristics for the design criteria of variable‐resolution climate model domains.