In the past decade, we have witnessed the widespread adoption of Deep Neural Networks (DNNs) in several Machine Learning tasks. However, in many critical domains, such as healthcare, finance, or law enforcement, transparency is crucial. In particular, the lack of ability to conform with prior knowledge greatly affects the trustworthiness of predictive models. This paper contributes to the trustworthiness of DNNs by promoting monotonicity. We develop a multi-layer learning architecture that handles a subset of features in a dataset that, according to prior knowledge, have a monotonic relation with the response variable. We use two alternative approaches: (i) imposing constraints on the model’s parameters, and (ii) applying an additional component to the loss function that penalises non-monotonic gradients. Our method is evaluated on classification and regression tasks using two datasets. Our model is able to conform to known monotonic relations, improving trustworthiness in decision making, while simultaneously maintaining small and controllable degradation in predictive ability.