Real networks often exhibit nontrivial topological features that do not occur in random graphs. The need for synthesizing realistic networks has resulted in development of various network models. In this paper, we address the problem of selecting and calibrating the model that best fits a given target network. The existing model fitting approaches mostly suffer from sensitivity to network perturbations, lack of the parameter estimation component, dependency on the size of the networks, and low accuracy. To overcome these limitations, we considered a broad range of network features and employed machine learning techniques such as genetic algorithms, distance metric learning, nearest neighbor classification, and artificial neural networks. Our proposed method, which is named ModelFit, outperforms the state-of-the-art baselines with respect to accuracy and noise tolerance in different network datasets.