Populist and governmental actors use emotional appeals to strategically influence voters and policy. Measuring populist rhetoric using text as data is far from trivial, however, because it is fundamentally oppositional and highly context dependent. Populist speech is oppositional in nature because it relies on the distinction between “the people” and the establishment, and it is context dependent because what constitutes opposition varies depending on the issue in question. Dictionary-based approaches are a transparent way of quantifying speech patterns, but they lack the ability to appropriately deal with the nuance and conditionality that defines political rhetoric. To overcome these issues, we use supervised machine learning to classify 1.6 million tweets about the Coronavirus pandemic by Conservative and Labour MPs in the United Kingdom, as well as Conservative and Labour sympathizers. Our classifier is based on expert coding of five thousand tweets about the Coronavirus pandemic and provides a fine-grained measure along four dimensions: issue, stance, type of rhetoric, and populist vs governmental orientation. Using this measure, we are able to analyze emotional appeals in populist rhetoric in much more detail than previous approaches. Hence, we provide a substantive analysis of populist rhetoric during the Coronavirus pandemic, and we conclude by offering technical guidance on the computational analysis of populist discourse using supervised machine learning.