In a manner relating to or according to the rules and practices of heraldry.
From 'heraldic' or 'heraldical' with the adverbial suffix '-ly' (from Old English '-lice'), which converts adjectives into adverbs describing how something is done.
When a historian says something is 'heraldically correct,' they mean it follows all those super-specific medieval rules about how coats of arms should look and be arranged.
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