Depends if you meant it as an interjection ("Seriously!": semicolon) or as an adverb ("Have you ever seriously heard ...": comma).

No one really uses semicolons any more, but they're interchangeable with periods. (Sorry: "full stops".) It just implies a closer relationship between the two sentences than a period might.

For example: "Bob was happy. The rain had stopped." vs. "Bob was happy; the rain had stopped." The latter implies that Bob was happy because the rain stopped. The former just expresses two separate ideas. A comma would be inappropriate and would turn the quote into a run-on sentence.