Rule number 1
Use a semicolon to combine two independent clauses that are closely connected in meaning.

Rule number 2
Use a semicolon before conjunctive adverbs when they are followed by an independent clause.
Conjunctive adverbs are used to connect one clause to another. Examples of conjunctives adverbs are however, furthermore, moreover, meanwhile, otherwise, nevertheless, besides, etc.
Examples:

John's at the top of his company's pay scale; Terri has to take a pay cut.
John's at the top of his company's pay scale; meanwhile, Terri has to take a pay cut.

You'll have to go now; you'll be late for work.
You'll have to go now; otherwise, you'll be late for work.

Juliet is very hardworking; she's not very creative.

Juliet is very hardworking; however, she’s not very creative.
Juliet is very hardworking; however, she’s not very creative.

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