Background: Magnetic resonance (MRI) scanning of the heart is an established part of the investigation of cardiovascular conditions in children. In young children, sedation is likely to be needed, and multiple controlled periods of apnea are often required to allow image acquisition. Suppression of spontaneous ventilation is possible with remifentanil; however, the dose required is uncertain. Aims: To establish the dose of remifentanil, by infusion, required to suppress ventilation sufficiently to allow a 30-s apnea during MRI imaging of the heart. Method: Patients aged 1–6 years were exposed to different doses of remifentanil, and the success in achieving a 30-s apnea was recorded. A dose recommendation was made for each patient, informed by responses of previous patients using an adaptive Bayesian dose-escalation design. Other aspects of anesthesia were standardized. A final estimate of the dose needed to achieve a successful outcome in 80% of patients (ED80) was made using logistic regression. Results: 38 patients were recruited, and apnea achieved in 31 patients. The estimate of the ED80 was 0.184 µg/kg/min (95% CI 0.178–0.190). Post hoc analysis revealed that higher doses were required in younger patients. Conclusion: The ED80 for this indication was 0.184 µg/kg/min (95% CI 0.178–0.190). This is different from optimal dosing identified for other indications and dosing of remifentanil should be specific to the clinical context in which it is used.