Capitalization after a semicolon in general correspondence.

No.

You do not capitalize after a semicolon unless, of course, what follows is a proper noun.

You don't, unless the word is capitalized anyway, such as I or Florida or a person's name. A semi-colon is not the end of a sentence; it's just the end of a clause.

reply to my results
Thank you all for your confirmation, I thought I was correct, howecer, I sometimes doubt my thoughts when I haven't done a thing in quite a while. I probably need to incorporate usage of semicolons into my writing more often to maintain rules properly, thank you once again and best.