Ref: Little Brown Handbook, 11th Ed. Pg. 444, 445; 671, Pearson Education (2010)
Use a semicolon between main clauses not joined by "and," "but," or another coordinating conjunction (LBH P.445).
Main clauses: contain a subject and a predicate and do not begin with a subordinating word (ie., examples of subordinating words: "when" Larry left; because Larry used it; whoever Larry called; as, if only, unless, now that [Larry left], etc.)
Example: Now that Larry watches the news, Bill makes news. [can't use a semi-colon] Why? Subordinating words "now that" changes the main clause to a subordinate clause. This now makes both clauses unequal. Since both clauses are now unequal, use a comma (P.444) (like I just did here - haha.)
To join two main clauses in a sentence, you have two primary options to separate them:
Insert a comma and a coordinating conjunction: and, but, or, nor, for, so, yet, etc. (445; 671) Example: Larry watches the news, so Bill makes news.
Insert a semicolon:
Example: Larry watches the news; Bill makes news.
The comma chiefly separates both equal and unequal sentence elements, while the semicolon primarily separates equal and balanced sentence elements (445)(key!)
Often the first clause creates some kind of expectation, and the second clause fulfills it. Advice is to use sparingly.