Predicting the motion of other road agents enables autonomous vehicles to perform safe and efficient path planning. This task is very complex, as the behaviour of road agents depends on many factors and the number of possible future trajectories can be considerable (multi-modal). Most prior approaches proposed to address multi-modal motion prediction are based on complex machine learning systems that have limited interpretability. Moreover, the metrics used in current benchmarks do not evaluate all aspects of the problem, such as the diversity and admissibility of the output. In this work, we aim to advance towards the design of trustworthy motion prediction systems, based on some of the requirements for the design of Trustworthy Artificial Intelligence. We focus on evaluation criteria, robustness, and interpretability of outputs. First, we comprehensively analyse the evaluation metrics, identify the main gaps of current benchmarks, and propose a new holistic evaluation framework. We then introduce a method for the assessment of spatial and temporal robustness by simulating noise in the perception system. To enhance the interpretability of the outputs and generate more balanced results in the proposed evaluation framework, we propose an intent prediction layer that can be attached to multi-modal motion prediction models. The effectiveness of this approach is assessed through a survey that explores different elements in the visualization of the multi-modal trajectories and intentions. The proposed approach and findings make a significant contribution to the development of trustworthy motion prediction systems for autonomous vehicles, advancing the field towards greater safety and reliability.