In this paper we criticize the robustness measure traditionally employed to assess the performance of machine learning models deployed in adversarial settings. To mitigate the limitations of robustness, we introduce a new measure called resilience and we focus on its verification. In particular, we discuss how resilience can be verified by combining a traditional robustness verification technique with a data-independent stability analysis, which identifies a subset of the feature space where the model does not change its predictions despite adversarial manipulations. We then introduce a formally sound data-independent stability analysis for decision trees and decision tree ensembles, which we experimentally assess on public datasets and we leverage for resilience verification. Our results show that resilience verification is useful and feasible in practice, yielding a more reliable security assessment of both standard and robust decision tree models.