Every exam system has its day. Board results in India, when a whole state refreshes the same website at once. Licensure results in the Philippines, with a list of names read by an entire family on one phone. GCSE and A-level mornings in August, envelopes and school halls. University finals, entrance exams, a driving test. The details change; the feeling does not.
The problem with what people usually say on results day is timing. Congratulations only work if they passed. Comfort only works if they did not. And whatever you say after you know the number sounds like it was shaped by the number.
A letter written in advance escapes that. You write it before anyone knows, which means your pride in the work, the late nights, the effort they gave is on record, fixed, and true in both outcomes. Many people write two: one to open if it goes well, and one to open if it does not, so the right words are already waiting whichever way the morning goes.
The best ones are short. One thing you noticed them doing while they studied, one sentence that is true whatever the score, and a plan for tonight that has nothing to do with exams.