<p>I understand your argument; but I often use “but” following a semicolon, though usually in cases where one of the two clauses has another comma in it. Sorry to repeat this, but the “however” at the end of the sentence just strikes me as awkward–though maybe SAT approves. What was the source of these items, and what is the answer given?</p>
<p>A Google search turned up
<a href=“http://www.grammar-monster.com/lessons/semicolons_before_conjunctions.htm[/url]”>http://www.grammar-monster.com/lessons/semicolons_before_conjunctions.htm</a>
as the top hit. This site oks coordinating conjunctions following semi-colons, even when the clauses themselves do not contain commas.</p>