Semicolons with Quotation Marks
Semicolons and colons always go outside the closing quotation mark, in every major style.
Unlike commas and periods, whose placement splits British and American practice, semicolons and colons are consistent worldwide: they sit outside the closing quotation mark unless they belong to the quoted material itself.
The rule is logical rather than typographic. A semicolon joins two clauses of your sentence, not of the quotation, so it belongs to your sentence and stands outside the quotation marks.
Write: She called the plan "unworkable"; the board approved it anyway. Never: She called the plan "unworkable;" the board approved it anyway.
Common mistake: extending the American 'periods and commas inside' habit to all punctuation. The American exception covers exactly two marks — the comma and the period.
“The memo described the budget as "provisional"; three departments had already spent it.”
Keep reading the glossary
The rule — differing on either side of the Atlantic — for where the comma and period sit relative to a closing quotation mark.
Placing punctuation inside quotation marks only when it belonged to the quoted material.
The punctuation that signals direct speech or a quoted phrase — single or double, depending on locale.
When to introduce quoted material with a colon rather than a comma or nothing at all.