We introduce a trusted infrastructure for symbolic analysis of modern event-driven Web applications. This infrastructure consists of reference implementations of the DOM Core Level 1 and UI Events, JavaScript Promises, and the JavaScript async/await APIs, all underpinned by a simple Core Event Semantics that is sufficiently expressive to describe the event models underlying all these APIs. Our reference implementations are trustworthy in that they follow the API respective standards line-by-line and they are thoroughly tested against the appropriate official test-suites, passing all the applicable tests. Using the Core Events Semantics and the reference implementations, we develop JaVerT.Click, a symbolic execution tool for JavaScript that, for the first time, supports reasoning about JavaScript programs that use some (possibly all) these APIs. Using JaVerT.Click, we perform comprehensive symbolic testing of the events module of Cash, a widely-used jQuery alternative, creating a symbolic test suite with 100% line coverage, establishing bounded correctness of several essential properties of the module, and discovering two subtle, previously unknown bugs.