I think it was released in the 2010s, maybe more than 15 years ago. The story is about a girl who practices kendo and meets a new transfer student from an elite school (possibly MIT). Together, they start solving mysteries. I remember one episode where the female lead was transported to the past and solved a case with a man who looked just like the transfer student from her school. In that episode, she also lost her phone in the past.

I personally haven't watched it but the synopsis and comments from users sounded like what you described: https://kisskh.at/461-q.e.d

THANKYOU! How did you manage to find it? 😊 I’m listening to the drama’s OST now. I used to love the song. Really appreciate your help!

You're welcome! I found it by luck using advance search and look for Japanese releases between 2005-2015. I don't remember what else I put on the search filters....lol