The recent scientific literature abounds in proposals of seizure forecasting methods that exploit machine learning to automatically analyze electroencephalogram (EEG) signals. Deep learning algorithms seem to achieve a particularly remarkable performance, suggesting that the implementation of clinical devices for seizure prediction might be within reach. However, most of the research evaluated the robustness of automatic forecasting methods through randomized cross-validation techniques, while clinical applications require much more stringent validation based on patient-independent testing. In this study, we show that automatic seizure forecasting can be performed, to some extent, even on independent patients who have never been seen during the training phase, thanks to the implementation of a simple calibration pipeline that can fine-tune deep learning models, even on a single epileptic event recorded from a new patient. We evaluate our calibration procedure using two datasets containing EEG signals recorded from a large cohort of epileptic subjects, demonstrating that the forecast accuracy of deep learning methods can increase on average by more than 20%, and that performance improves systematically in all independent patients. We further show that our calibration procedure works best for deep learning models, but can also be successfully applied to machine learning algorithms based on engineered signal features. Although our method still requires at least one epileptic event per patient to calibrate the forecasting model, we conclude that focusing on realistic validation methods allows to more reliably compare different machine learning approaches for seizure prediction, enabling the implementation of robust and effective forecasting systems that can be used in daily healthcare practice.