Due to the success of formal modeling of protocols such as TLS, there is a revival of interest in applying formal modeling to standardized APIs. We argue that formal modeling should happen as the standard is being developed (not afterwards) as it can detect complex or even simple attacks that the standardization group may not otherwise detect. As a case example of this, we discuss in detail the W3C Web Cryptography API. We demonstrate how a formal analysis of the API using the modeling language AVISPA with a SAT solver demonstrates that while the API has no errors in basic API operations and maintains its security properties for the most part, there are nonetheless attacks on secret key material due to how key wrapping and usages are implemented. Furthermore, there were a number of basic problems in terms of algorithm selection and a weakness that led to a padding attack. The results of this study led to the removal of algorithms before its completed standardization and the removal of the padding attack via normalization of error codes, although the key wrapping attack is still open. We expect this sort of formal methodology to be applied to new standardization efforts at the W3C such as the W3C Web Authentication API.