Artificial intelligence (AI) systems are increasingly used in healthcare applications, although some challenges have not been completely overcome to make them fully trustworthy and compliant with modern regulations and societal needs. First of all, sensitive health data, essential to train AI systems, are typically stored and managed in several separate medical centers and cannot be shared due to privacy constraints, thus hindering the use of all available information in learning models. Further, transparency and explainability of such systems are becoming increasingly urgent, especially at a time when “opaque” or “black-box” models are commonly used. Recently, technological and algorithmic solutions to these challenges have been investigated: on the one hand, federated learning (FL) has been proposed as a paradigm for collaborative model training among multiple parties without any disclosure of private raw data; on the other hand, research on eXplainable AI (XAI) aims to enhance the explainability of AI systems, either through interpretable by-design approaches or post-hoc explanation techniques. In this paper, we focus on a healthcare case study, namely predicting the progression of Parkinson’s disease, and assume that raw data originate from different medical centers and data collection for centralized training is precluded due to privacy limitations. We aim to investigate how FL of XAI models can allow achieving a good level of accuracy and trustworthiness. Cognitive and biologically inspired approaches are adopted in our analysis: FL of an interpretable by-design fuzzy rule-based system and FL of a neural network explained using a federated version of the SHAP post-hoc explanation technique. We analyze accuracy, interpretability, and explainability of the two approaches, also varying the degree of heterogeneity across several data distribution scenarios. Although the neural network is generally more accurate, the results show that the fuzzy rule-based system achieves competitive performance in the federated setting and presents desirable properties in terms of interpretability and transparency.