How did my aunt express congratulations after I passed the exam?

The choice that states "congratulated me on having passed" accurately captures the specific action of expressing congratulations in a direct manner. The phrase clearly indicates that the aunt formally acknowledged the achievement of passing the exam, which is essential in reflecting the intent behind the congratulations.

The other choices, while related to expressing good wishes or acknowledgment of success, do not precisely convey the act of congratulating someone. For instance, saying "remarked on my passing" suggests a comment or observation rather than a direct expression of congratulations. "Praised me for passing" implies a judgment of quality, which, while positive, doesn't necessarily convey the traditional congratulatory sentiment. Lastly, "celebrated with me on passing" suggests a shared experience or festivity, but it does not mean directly expressing congratulations, which is the core of the original question. Hence, the best choice here is the one that directly indicates congratulations.