In recent years, convolutional neural networks (CNNs) have achieved significant success in various synthetic aperture radar (SAR) tasks. However, the complexity and opacity of their internal mechanisms hinder the fulfillment of high-reliability requirements, thereby limiting their application in SAR. Improving the interpretability of CNNs is thus of great importance for their development and deployment in SAR. In this paper, a visual explanation method termed multi-weight self-matching class activation mapping (MS-CAM) is proposed. MS-CAM matches SAR images with the feature maps and corresponding gradients extracted by the CNN, and combines both channel-wise and element-wise weights to visualize the decision basis learned by the model in SAR images. Extensive experiments conducted on a self-constructed SAR target classification dataset demonstrate that MS-CAM more accurately highlights the network's regions of interest and captures detailed target feature information, thereby enhancing network interpretability. Furthermore, the feasibility of applying MS-CAM to weakly-supervised obiect localization is validated. Key factors affecting localization accuracy, such as pixel thresholds, are analyzed in depth to inform future work.