Accurate forecasts of containerised freight volumes are unquestionably important for port terminal operators to organise port operations and develop business plans. They are also relevant for port authorities, regulators, and governmental agencies dealing with transportation. In a time when deep learning is in the limelight, owing to a consistent strip of success stories, it is natural to apply it to the tasks of forecasting container throughput. Given the number of options, practitioners can benefit from the lessons learned in applying deep learning models to the problem. Coherently, in this work, we devise a number of multivariate predictive models based on deep learning, analysing and assessing their performance to identify the architecture and set of hyperparameters that prove to be better suited to the task, also comparing the quality of the forecasts with seasonal autoregressive integrated moving average models. Furthermore, an innovative representation of seasonality is given by means of an embedding layer that produces a mapping in a latent space, with the parameters of such mapping being tuned using the quality of the predictions. Finally, we present some managerial implications, also putting into evidence the research limitations and future opportunities.