If the sentence fragment would be considered stylistically acceptable on its own, then using a semicolon wouldn't be obviously wrong.
For instance:
"How much do they cost?"
"Maybe $10."
Maybe $10, even though it's a sentence fragment and would not be acceptable as a standalone sentence, is acceptable in that dialogue exchange.
An expanded version could be considered in the same light:
"How much do they cost?"
"They're not very expensive; maybe $10."
If the fragment is okay on its own as a reply, I would argue that the longer version, with the semicolon, shouldn't be immediately ruled out.
However, this still remains a matter of style. (Style overruling conventional use in this particular context.) It might simply look strange to use a semicolon in this situation—regardless of whatever reasoning that says it should be okay or at least not immediately wrong.
It's probably more common to use a dash or an actual period:
"How much do they cost?"
"They're not very expensive—maybe $10."
"How much do they cost?"
"They're not very expensive. Maybe $10."
So, in terms of style, first determine if the sentence fragment can actually be used at all. (And that would depend on style guides, the audience, and your personal opinion.) Once that's determined, decide which punctuation looks best.
But, as a matter of style, this is subjective.