Although deep learning has enabled a huge leap forward in image inpainting, current methods are often unable to synthesize realistic high-frequency details. In this paper, we propose applying super-resolution to coarsely reconstructed outputs, refining them at high resolution, and then downscaling the output to the original resolution. By introducing high-resolution images to the refinement network, our framework is able to reconstruct finer details that are usually smoothed out due to spectral bias - the tendency of neural networks to reconstruct low frequencies better than high frequencies. To assist training the refinement network on large upscaled holes, we propose a progressive learning technique in which the size of the missing regions increases as training progresses. Our zoom-in, refine and zoom-out strategy, combined with high-resolution supervision and progressive learning, constitutes a framework-agnostic approach for enhancing high-frequency details that can be applied to any CNN-based inpainting method. We provide qualitative and quantitative evaluations along with an ablation analysis to show the effectiveness of our approach. This seemingly simple, yet powerful approach, outperforms state-of-the-art inpainting methods.