If you liked the Air anime, the Anime-Planet community thinks you'd like:
In the wake of a rebellion that shook Japan twenty years prior, Togame Hida, general director and strategist for the army, seeks to obtain the 12 "deviant blades" created by master swordsmith Shikizaki Kiki to help add stability and security to the Bakufu government. To aid in this endeavor, she looks to enlist the help of Yasuri Mutsune, head of the Kyotou-ryu school and hero of the rebellion. But when she arrives on the island where he lives in exile, she finds him dead, succeeded by his skilled yet slightly daft son Shichika. Undeterred, the two set off from the island in search of the swords armed only with Togami's sharp strategic mind and Shichika's powerful, swordless Kyotou-ryu.
While there are several differences between the two one thing that they both have in common is that right from the beginning they get the viewer interested in the characters and what happens to them. In addition both feature overall plots that span the time of a couple centuries but at the same time focusing on primarily on a pair on two people. Though Katanagatari does have some action in it and Air is just overall slow-paced if you liked one then you'll probably be interested in the other.
As scientists explore a new form of energy on the moon, an experiment gone awry brings the lead scientist's life crashing to a halt. In a freak accident, his daughter Kurau is engulfed in the energy and becomes the mysterious entity known as Rynax; a pairing that endows her with new superhuman abilities and a new personality. Years later, Kurau is using her unique powers to make a living as a bounty hunter, but the corporation has not given up on this new form of energy and will stop at nothing to find her. Now, Kurau must protect not only herself, but her Rynax "pair" named Christmas, a soul mate more precious to her than life itself. Can Kurau and Christmas find peace for themselves and the Rynax?
Despite being quite different if taken at face value, both Kurau and Air have one major thing in common: the incredible story that focuses on what it means to be family. I recommend that if you like one, you will like the other, as the stories will really tug at your heart.
What starts as a simple interview of a legendary actress becomes a journey through the history of Japan. But this is no ordinary lesson; from the perspective of this actress, we learn of the beauty and sadness of love, the pain and regret and joy of the Japanese people and their film, through this film: Millennium Actress.
As the school term draws to a close, Koutarou Makimura vows to confess his love to Kaho Serizawa, the most beautiful girl in school. However, on the way home, he accidentally fondles a time traveler named Ligene, causing her to strike him recklessly over the head with an hourglass. When Koutarou wakes up, he discovers that summer has been and gone and that Kaho has tragically died. Now, with Ligene's help, he must leap through time and change the events of summer in order to save Kaho from her fate.
In the Heian period, political instability within the capital is beginning to manifest amidst widespread famine and disease. In order to stem the growing chaos, the Emperor orders Minamoto no Raikou -- a man known for his archery skills -- to reclaim the magatama, a mysterious jewel said to contain the power to save the world. But when Raikou himself becomes ill, it falls to his younger sister, Hikaru, to disguise herself and take her brother's place. In her quest for the magatama, Hikaru finds herself and her companions drawn deeper into a struggle she cannot comprehend...
These two anime are quite different, but if youlike your anime to have some historical perspective in regards to Japanese folklore than these two fit well together. If you like to anime to take a surprising twist, which I will not dare to reveal in even the slightest fashion then these two also fit well together, for both are transformed somewhere around the middle becoming something quite different, but certainly wonderful.