A fee or tax paid for the use of a harbor or haven; the right to use port facilities.
From 'haven' (a harbor, shelter) plus '-age' (a fee, tax, or right to do something). This word follows the pattern of medieval commercial terms like 'wharfage' and 'anchorage,' combining location with payment.
Medieval ports had a dizzying array of fees—'havenage' was just one of many charges a ship owner faced, along with wharfage, anchorage, and lighterage! These words show how specialized port economies had their own vocabulary.
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