In the last article on the semicolon, we covered how it’s used as a kind of “meta-comma,” separating list items that already have commas themselves.  The second of the two uses requires a definition: the clause. In grammatical terms, a clause has a subject and a verb. Clauses are either independent or dependent; independent clauses can stand on their own as complete sentences ( . . . which is why they’re labeled “independent”), while dependent clauses cannot.

Do you need to know that in order to use semicolons correctly? No, but some people like to know that sort of thing.

the empire strikes back
I ate all of my pudding
where is that darn cat?
leave it to Beaver
girls rock

Independent clauses (“complete sentences”):

Dependent clauses (not complete sentences):

while you were sleeping
when Harry met Sally
ever since I bought that monkey
because the fuzz gives me the chills

(You might have noticed that if you were to take away the first word or two from each of those dependent clauses, you would have an independent clause again [“Harry met Sally”]; that’s a topic for another time. Our topic is semicolons!)

So, simply put: if the clause on each side of the typographical spot in question is an independent clause – if each of them can stand alone as a complete sentence – if you could sleep at night knowing you put a period and a capital letter there instead, then you can put a semicolon in there. If not, you can’t. Stylistically, some places are better for semicolons than others, of course, but the two parts connected by a semicolon should be related in some way, connected a little more closely than a period would suggest in the same place.

We’ve covered the rules, and how they can help your writing, but what about the test? Take this GMAT-type Sentence Correction question as an example:

The chairman of the board, who was very sorry to learn that he’d acted on incorrect information, should not be held responsible to decreasing revenues or falling stock prices; though many have suggested he should.

A. should not be held responsible to decreasing revenues or falling stock prices; though

B. should not be in a position of responsibility for decreasing revenues or falling stock prices, though

C. should not be held responsible for decreasing revenues or falling stock prices, though

D. was not to be held responsible for decreasing revenues or falling stock prices; though

E. was not to be held responsible to decreasing revenues or falling stock prices, though

One of the main Sentence Correction tactics is the elimination of repeated errors vertically in the answers, improving your odds dramatically. When faced with a semicolon (or more than one) in the answer choices, your instinctive reaction should be to judge quickly whether the clauses on both sides are independent; if both clauses are not, that answer with the semicolon is incorrect. Be careful; some Sentence Correction questions make more changes from answer to answer, so crossing off one choice with a semicolon does not automatically enable you to cross them all off.

In this question, ignoring the other errors, we see A and D have a semicolon before “though;” we react by distilling the sentence down to its bare minimum: “The chairman should not be held responsible; though many have suggested he should.” Is “the chairman should not be held responsible” able to stand on its own as a sentence? Yes, it is! Is “though many have suggested he should” able to stand alone as a sentence? No, it cannot – so we can eliminate choices A and D, improving our odds of getting the correct answer to 1 in 3, and we still have to look at the other errors! 
See the first article in this series:
The Semicolon: Not Just Another Winky Face, Part I