The trustworthiness and safety of an electronic system can be compromised by a harsh electromagnetic environment. Additionally, an electronic system may experience various types of failures under electromagnetic disturbances, resulting in varying levels of (un)reliable operation. To address this, this paper proposes the use of a testing-to-failure approach for characterising the susceptibility profiles of a medical monitoring system as an example. The approach is practically applied to the system under different modulated continuous wave electromagnetic disturbances, resulting in classified immunity test profiles indicating the severity of the occurring failures. These profiles are further analysed and compared among various types of disturbances.