The search for energy efficient circuital implementations of neural networks has led to the exploration of phase-change memory (PCM) devices as their synaptic element, with the advantage of compact size and compatibility with CMOS fabrication technologies. In this work, we describe a methodology that, starting from measurements performed on a set of real PCM devices, enables the training of a neural network. The core of the procedure is the creation of a computational model, sufficiently general to include the effect of unwanted non-idealities, such as the voltage dependence of the conductances and the presence of surrounding circuitry. Results show that, depending on the task at hand, a different level of accuracy is required in the PCM model applied at train-time to match the performance of a traditional, reference network. Moreover, the trained networks are robust to the perturbation of the weight values, up to 10% standard deviation, with performance losses within 3.5% for the accuracy in the classification task being considered and an increase of the regression RMS error by 0.014 in a second task. The considered perturbation is compatible with the performance of state-of-the-art PCM programming techniques.