This paper proposes a damage detection procedure based on neural networks that is able to account for the model error in the network training. Vibration-based damage detection procedures relied on machine learning techniques hold great promises for the identification of structural damage thanks to their efficiency even in presence of noise-corrupted data. However, it is rarely possible in the context of civil engineering to have large amount of data related to the damaged condition of a structure to train a neural network. Numerical models are then necessary to simulate damaged scenarios. However, even if a finite element model is accurately calibrated, experimental results and model predictions will never exactly match and their difference represents the model error. Being the neural network tested and trained with respect to the data generated from the numerical model, the model error can significantly compromise the effectiveness of the damage detection procedure. The paper presents a procedure aimed at mitigating the effect of model errors when using models associated to the neural network. The proposed procedure is applied to two case studies, namely a numerical case represented by a steel railway bridge and a real structure. The real case study is a steel braced frame widely adopted as a benchmark structure for structural health monitoring purposes. Although in the first case the procedure is carried out considering simulated data, we have taken into account some key aspects to make results representative of real applications, namely the stochastic modelling of measurement errors and the use of two different numerical models to account for the model error. Different networks are investigated that stand out for the preprocessing of the dynamic features given as input. Results show the importance of accounting for the model error in the network calibration to efficiently identify damage.