Coronary artery stenosis is a common cardiovascular disease, with severe, untreated cases posing significant risks of heart attack. Although coronary (X-ray) angiograms remain the standard for stenosis diagnosis, they are invasive, time- and resource-intensive, and therefore only performed on patients with a high probability of disease based on symptoms and prior clinical tests. However, a subset of patients, especially those without symptoms, may remain undiagnosed. Detecting indications of stenosis from ECGs, which are fast, cheap, non-invasive, and thus routinely acquired even in asymptomatic patients, would support early diagnosis. However, as no reliable stenosis-specific signal has been identified in ECGs, they can not currently be used for stenosis risk stratification. To address this, we introduce StenCE, a pretraining framework, allowing stratification of patients based on features derived directly from ECGs. Evaluations across varying stenosis severity thresholds and additional ECG disease classification tasks demonstrate consistent performance improvements across different ECG encoders, outperforming previous work. The obtained models successfully detect signals for stenosis diagnosis in ECGs and are the first to achieve high performance in severe stenosis classification. The source code is available at https://github.com/NikolaCenic/ecg-stenosis-cls.