Kendo Rage, or Makeruna! Makendō (負けるな!魔剣道, "Do Not Lose! Kendo Magic") stars, in its original Japanese version, a girl named Mai Tsurugino (剣野 舞 Tsurugino Mai). A spirit detective named Doro (ドロ) finds Mai and asks her to help him attack monsters.
A sequel was made on the Super Famicom and PlayStation and subsequently named Makeruna! Makendō 2, but plays as a head-to-head fighting game. An RPG named Makeruna! Makendō Z was released for the PC-FX.
There was also an Anime OVA based on the game called "Don't Lose Makendo" which follows more closer to the original Japanese version of the game which features both Mai and her younger sister Hikari (the main character from the second game).
Source: Wikipedia, "Kendo Rage", available under the CC-BY-SA License.