Semi-formal, to me, screams black Barathea Argyll jacket with/without waistcoat and a nice necktie. Though, I think a nice charcoal tweed would work as well. If the event was on the less than semi-formal side, I might consider just a waiscoat/tie combo or just a shirt and tie. If the invitation says semi-formal, I would assume I should wear a jacket. I would tend to think that one step down from "black tie" would be the way to go.