Synthetic aperture radar (SAR) image super-resolution (SR) has broad application prospects in military reconnaissance, marine monitoring, crop monitoring, and other fields. However, when the scale factor is large, current SAR image SR has limitations, such as insufficient feature extraction, difficulty of feature representation, and modeling difficulty of SR reconstruction. These problems have severely restricted the SR performance of SAR images. In addition, optical remote sensing images share higher resolution and richer high-frequency information than SAR remote sensing images. Therefore, we adopt high-resolution (HR) optical images as auxiliary images of SAR image SR to improve the performance of SAR image SR. Our research is conducted from two aspects: the extraction efficiency of HR optical image-guided information and the representation ability of low-resolution (LR) SAR image features. We propose an optical guidance residual networks (OGRNs) based on residual learning for SAR image SR. The OGRN uses optical images during network training, which enhances the performance of SAR image SR, even when optical images are missing during network testing. First, we extract the texture feature of SAR images through the designed residual learning module. Second, we extract the weight map of feature information for SAR image SR from HR optical images by the convolutional layer. Finally, the weight map is used to guide the weighted supervised SR reconstruction for SAR images. Extensive experimental results demonstrated that, under the guidance of optical images, OGRN achieves excellent performance in terms of both quantitative assessment metrics and visual quality.