I know the basics of a semicolon—at least I think I do. Aside from delimiting verbose lists, it separates independent clauses of a sentence. So, if you have two independent clauses in a sentence, you can either separate them with a semicolon, or a comma along with a conjunction, like "but".

However, I've noticed a few authors actually using a semicolon with a conjunction, like:

<independent clause 1>; but <independent clause 2>

Can anyone shed some light on when this is preferable to just a comma? Is this simply a matter of personal preference?

(I purposefully left out any real-life examples because I don't want to influence the answers I get)

Thanks!