In artificial neural networks, understanding the contributions of input features on the prediction fosters model explainability and delivers relevant information about the dataset. While typical setups for feature importance ranking assess input features individually, in this study, we go one step further and rank the importance of groups of features, denoted as feature-blocks. A feature-block can contain features of a specific type or features derived from a particular source, which are presented to the neural network in separate input branches (multiblock ANNs). This work presents three methods pursuing distinct strategies to rank features in multiblock ANNs by their importance: (1) a composite strategy building on individual feature importance rankings, (2) a knock-in, and (3) a knock-out strategy. While the composite strategy builds on state-of-the-art feature importance rankings, knock-in and knock-out strategies evaluate the block as a whole via a mutual information criterion. Our experiments consist of a simulation study validating all three approaches, followed by a case study on two distinct real-world datasets to compare the strategies. We conclude that each strategy has its merits for specific application scenarios.