Shakugan no Shana, Noragami Recommendations
Both have supernatural creatures and another invisible "world" that cannot be seen by normal humans. Both have normal people forgetting the presence of people that were affected by the "other world." Both MCs have long "katana like" swords. The flame hazes can be the gods of Noragami. Both have a girl that doesn't fight but gets involved with the "other world." Both have antagonists that have many "pawns/weapons."
Flame Haze are basically Gods of Noragami. Both anime have two MC's. One who is a God/FH, and one who is a human. Both God/FH have a katana that is the spirit of a human, that they use to hunt demons, aka Ayakashi/Denizens. Yato gets into fights with other Gods they the same as Shana does with other Flame Haze. Both human MC's run into the God/FH and acquire a power that allows them see and interact with these other worldly spirits, and get caught up in the middle of the fights.
Main difference between the two, is Noragami has terrible pacing, vague character development,
Very similar concept and an amazing watch
Human-supernatural border clash. Shakugan no Shana and Noragami, both focus on the stories of Yuuji and Hiyori as they become entangled with the affairs of Shana and Yato respectively.
Though Noragami presents itself as a story of which involve the odd adventures of Yato's group it does look deep into its characters and their motives. With Shakugan no Shana, it is more of the journey of Yuuji with Shana as he explores the world of the Flame Hazes and fragile relationships with the human world.