Camera model identification refers to the problem of linking a picture to the camera model used to shoot it. In this paper, as this might be an enabling factor in different forensic applications to single out possible suspects (e.g., detecting the author of child abuse or terrorist propaganda material), many accurate camera model attribution methods have been developed. One of their main drawbacks, however, are a typical closed-set assumption of the problem. This means that an investigated photograph is always assigned to one camera model within a set of known ones present during the investigation, i.e., training time. The fact that a picture can come from a completely unrelated camera model during actual testing is usually ignored. Under realistic conditions, it is not possible to assume that every picture under analysis belongs to one of the available camera models. In this paper, to deal with this issue, we present an in-depth study on the possibility of solving the camera model identification problem in open-set scenarios. Given a photograph, we aim at detecting whether it comes from one of the known camera models of interest or from an unknown one. We compare different feature extraction algorithms and classifiers especially targeting open-set recognition. We also evaluate possible open-set training protocols that can be applied along with any open-set classifier, observing that a simple alternative among the selected ones obtains the best results. Thorough testing on independent datasets show that it is possible to leverage a recently proposed convolutional neural network as feature extractor paired with a properly trained open-set classifier aiming at solving the open-set camera model attribution problem even on small-scale image patches, improving over the state-of-the-art available solutions.