Modern infrastructures are becoming increasingly dependent on electronic systems, leaving them more vulnerable to electrical surges or electromagnetic interference. Electromagnetic disturbances appear in nature, e.g., lightning and solar wind; however, they may also be generated by man-made technology to maliciously damage or disturb electronic equipment. This article presents a systematic risk assessment framework for identifying possible, consequential, and plausible intentional electromagnetic interference (IEMI) attacks on an arbitrary distribution network infrastructure. In the absence of available data on IEMI occurrences, we find that a systems-based risk assessment is more useful than a probabilistic approach. We therefore modify the often applied definition of risk, i.e., a set of triplets containing scenario, probability, and consequence, to a set of quadruplets: scenario, resource requirements, plausibility, and consequence. Probability is "replaced" by resource requirements and plausibility, where the former is the minimum amount and type of equipment necessary to successfully carry out an attack scenario and the latter is a subjective assessment of the extent of the existence of attackers who possess the motivation, knowledge, and resources necessary to carry out the scenario. We apply the concept of intrusion areas and classify electromagnetic source technology according to key attributes. Worst-case scenarios are identified for different quantities of attacker resources. The most plausible and consequential of these are deemed the most important scenarios and should provide useful decision support in a countermeasures effort. Finally, an example of the proposed risk assessment framework, based on notional data, is provided on a hypothetical water distribution network.