Except when used to separate items in a series, a semicolon must be followed by an independent clause or else you create a sentence fragment.
I expected to win the debate; even if my opponent had more experience. (sentence fragment)
I had studied the subject thoroughly; and researched even the minor points. (sentence fragment)
These sentences could be corrected either by changing the punctuation within the sentence or by making the second clause independent.
I expected to win the debate, even if my opponent had more experience. (correct)
I had studied the subject thoroughly; I had researched even the minor points. (correct)