Accurately estimating the worst-case execution time (WCET) of real-time event-driven software is crucial. For example, NASA's study of unintended acceleration in Toyota vehicles highlights poor support in timing analysis for event-driven code, which could put human life in danger. WCET occurs during the longest possible execution path in a program. Static analysis produces safe but overestimated measurements. Dynamic analysis, on other hand, measures actual execution times of code under a test suite. Its performance depends on the branch coverage, which itself is sensitive to scheduling of events. Thus dynamic analysis often underestimates the WCET. We present a new dynamic approach called event-driven directed testing. Our approach combines aspects of prior random-testing techniques devised for event-driven code with the directed testing method applied to sequential code. The aim is to come up with complex event sequences and choices of parameters for individual events that might result in execution times closer to the true WCET. Our experiments show that, compared to random testing, genetic algorithms, and traditional directed testing, we achieve significantly better branch coverage and longer WCET.