Ultra_DTA: I'm a huge fan of console turn based strategy like Advanced Wars and Fire Emblem.
The closest to Fire Emblem you'll find here might be
Expedition Conquistador and
Banner Saga, both turn-based tactical games with some RPG elements (make choices between battles and live with the consequences), and both good games. Conquistador has exploration, while Banner has a strong story. Both have very cool tactical battles
Silent Storm has some very nice turn based tactics, too, with fun things like destructible environments. Some balance problems during the campaign, though (some classes have trouble leveling, and some late-game elements are somewhat unbalanced).
Going into older titles, my personal recommandation is
Jagged Alliance 2. Hire mercenaries and send them on an island to overthrow a psychotic dictator. One of my 10 favourite games ever :) (the first title did not age too well, but the second one is simply perfection)
There are other strategy games with turn-based battles (the Age of Wonders series is very good, for example), but they are not as "close and pesonnal" as those.
EDIT : Oh, and you might want to check the battle Isle games, since Advance Wars is basically a clone of those. Beware, though, those are some very old games, and the UI might be quite obsolete for people used to the niceties of modern games.