In this paper, twin-systems are described to address the eXplainable artificial intelligence (XAI) problem, where a black box model is mapped to a white box “twin” that is more interpretable, with both systems using the same dataset. The framework is instantiated by twinning an artificial neural network (ANN; black box) with a case-based reasoning system (CBR; white box), and mapping the feature weights from the former to the latter to find cases that explain the ANN’s outputs. Using a novel evaluation method, the effectiveness of this twin-system approach is demonstrated by showing that nearest neighbor cases can be found to match the ANN predictions for benchmark datasets. Several feature-weighting methods are competitively tested in two experiments, including our novel, contributions-based method (called COLE) that is found to perform best. The tests consider the ”twinning” of traditional multilayer perceptron (MLP) networks and convolutional neural networks (CNN) with CBR systems. For the CNNs trained on image data, qualitative evidence shows that cases provide plausible explanations for the CNN’s classifications.