As we rely on machine learning (ML) models to make more consequential decisions, the issue of ML models perpetuating unwanted social biases has come to the fore of the public's and the research community's attention. In this paper, we focus on the problem of detecting violations of individual fairness in ML models. We formalize the problem as measuring the susceptibility of ML models against a form of adversarial attack and develop a suite of inference tools for the adversarial loss. The tools allow practitioners to assess the individual fairness of ML models in a statistically-principled way: form confidence intervals for the adversarial loss and test hypotheses of model fairness with (asymptotic) non-coverage/Type I error rate control. We demonstrate the utility of our tools in a real-world case study.