Accuracy plays a central role in developing models of continuous physical systems, both in the context of developing a new model to fit observation or approximating an existing model to make analysis faster. The need for simple, yet sufficiently accurate, models pervades engineering analysis, design, and diagnosis tasks. This paper focuses on two issues related to this topic. First, it examines the process by which idealized models are derived. Second, it examines the problem of determining when an idealized model will be sufficiently accurate for a given task in a way that is simple and doesn’t overwhelm the benefits of having a simple model. It describes IDEAL, a system which generates idealized versions of a given model and specifies each idealized model’s credibility domain. This allows valid future use of the model without resorting to more expensive measures such as search or empirical confirmation. The technique is illustrated on an implemented example.