I don't think there's anything really quite like Kalafina out there, it's part of why I love them so much. There are, however, numerous artists which show some huge talent and I'd be happy to recommend a few.
Eiko Shimamiya is one such artist, back before I found out about Kalafina I had Shimamiya as my favourite Japanese artist. She disappeared for a short while to deal with thyroid cancer but seems to have returned with a few things recently, which pleases me greatly. She's got some very interesting concepts in her music and it sounds pretty unique, plus her voice is amazing when it's at its best. I'd recommend her albums 'O' and 'Hikari Nadeshiko'.
Akiko Shikata is another favourite of mine, bringing a style of music I'm not even sure how to describe apart from 'somewhat folky'. As with Eiko, her music is very unique and I can't think of anyone else that does anything even remotely similar. Give 'Raka' and 'Harmonia' a try.
In a somewhat similar vein, I'd recommend Rurutia as well. Electronica-infused pop music combined with whispery vocals is something that I've seen done by quite a few artists, but she does it better than most. It's got a certain ethereal atmosphere to it that I really like and frankly I just really like whispery vocals. Etsuko Yakushimaru appeals to me for similar reasons.
Recently I've been really quite impressed with OLIVIA's album 'The Lost Lolli', but OLIVIA (Olivia Lufkin) is only half-Japanese and the album is sung in English, so I don't know if that's quite what you want. She has done some Japanese stuff on the album 'OLIVIA inspi' REIRA (TRAPNEST)', featuring music for the anime NANA.
Since you're already interested in FictionJunction and Kalafina, I'll recommend Kaori Oda's 'Colors' album as well if you haven't heard it yet.
I find ClariS rather enjoyable too, their music isn't exactly anything original even in the electropop genre, but it's good quality material, often catchy as hell and they've got good vocal capabilities, which helps a lot. I'd say any of their three albums 'Birthday', 'Second Story' or 'Party Time' are good enough places to start. On the topic of electropop, Perfume are great too. '
⊿' is their most consistent and probably the best place to start.
As for other vocalists that may be worth checking out: Anna Tsuchiya, KOKIA, Shoko Nakagawa, KOTOKO, Yui Sakakibara, Maon Kurosaki, Kanako Ito, ROUNDTABLE feat. Nino, Rie Fu and Nagi Yanagi have all pleased my ears over the years.
Somewhat off topic, but also going to recommend Secret Messenger here, as they create arrangements of music from the Touhou games inspired heavily by Kajiura's style and damn do they do a good job of it. Not exactly the easiest of material to find, but there is some up on Youtube at the very least. Check out fromadistance too, easily some of the most unique arrangements around using traditional instruments and creating some form of classical folk style music which is really interesting. Same goes for Tutti Sound, who arrange music in the style of dramatic film trailer scores.
Oh and not Japanese but has done work for anime at least and I believe should be mentioned, ORIGA. Some of the most amazing vocals around.
