If you're looking for anime similar to Saki: The Nationals, you might like these titles. All recommendations are made by Anime-Planet users like you!
Forget track and field! At Oorai Girls Academy, they practice Shensha-do, the art of tank combat! But Miho transfers there believing it to be the one school where Shensa-do isn't offered. She's in for a rude awakening, however, when the student council president demands her participation in the sport. Together with four friends, she learns to face her fears, find herself, and have a whole lot of fun along the way. Get ready for tank fighting mayhem in Girls Und Panzer!
These shows both gave me the same vibe; they both focus around a talented girl who joins a high school club and enters in a competative tournament with a rookie team. Although the types of tournaments are really different the huge female casts and small amounts of fan-service make me think if you enjoyed one you might enjoy the other.
Move over, solitaire! Cardfight Vanguard is the card game that all the kids these days are playing. Using carefully prepared decks, players battle it out for fame and glory – the first to receive six damage points loses. After a bully takes Aichi's special card, the boy learns Vanguard to win it back and finds himself inexplicably drawn into the sport. Now determined to prove his skills to himself, as well as to the legendary player Toshiki Kai, Aichi climbs the ranks of Vanguard, making new friends and challenging fierce competitors along the way.
While Vanguard definitely has a more shounen/kiddy feel, both of these titles have an extremely similar format, and will likely appeal to the same kind of person. Each watches a group of students take on others in a tournament setting, with a single match usually drawing out over multiple episodes, with plenty of commentary from a pair of announcers.
[note: I usually don't recommend a later franchise title as a two-way rec, but I haven't seen the original Saki series, just Nationals]