Creating super-resolution cloth animations, which refine coarse cloth meshes with fine wrinkle details, faces challenges in preserving spatial consistency and temporal coherence across frames. In this paper, we introduce a general framework to address these issues, leveraging two core modules. The first module interleaves a simulator and a corrector. The simulator handles cloth dynamics, while the corrector rectifies differences in low-frequency features across various resolutions. This interleaving ensures prompt correction of spatial errors from the coarse simulation, effectively preventing their temporal propagation. The second module performs mesh-based super-resolution for detailed wrinkle enhancements. We decompose garment meshes into overlapping patches for adaptability to various styles and geometric continuity. Our method achieves an 8× improvement in resolution for cloth animations. We showcase the effectiveness of our method through diverse animation examples, including simple cloth pieces and intricate garments.