The predominant de facto paradigm of testing ML models relies on either using only held-out data to compute aggregate evaluation metrics or by assessing the performance on different subgroups. However, such data-only testing methods operate under the restrictive assumption that the available empirical data is the sole input for testing ML models, disregarding valuable contextual information that could guide model testing. In this paper, we challenge the go-to approach of data-only testing and introduce Context-Aware Testing (CAT) which uses context as an inductive bias to guide the search for meaningful model failures. We instantiate the first CAT system, SMART Testing, which employs large language models to hypothesize relevant and likely failures, which are evaluated on data using a self-falsification mechanism. Through empirical evaluations in diverse settings, we show that SMART automatically identifies more relevant and impactful failures than alternatives, demonstrating the potential of CAT as a testing paradigm.