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Erm, it's noted that Dumbledore did 'things with a wand that [an examiner] had never seen before' so I think it's clear that N.E.W.T's had a practical exam and were in fact overseen by Ministry...

I always figured that blood testing would be a (relatively) common thing in the Wizarding world for diagnoses. I mean, aren't children of werewolves in danger of being born as one? Maybe it's just an...