Samurai are a well-known part of Japanese history. Although they may be long gone, many of their martial arts and skills are still being taught. You can see for yourself the skill it takes to wield a sword with precision.
In Tokyo, join a dojo (practice hall) for your swordsmanship experience. Your instructor will first demonstrate the art of shizan (trial cutting) and you will then be given the chance to actually cut with a real sword. With clear and correct instruction, this experience will allow you to learn from the relative few with this skill and widen your horizons.
If you are looking for an active experience suitable for the whole family, in Kyoto the Toei Eigamura film studio will give you the chance to learn the basics of samurai sword fighting with film-set style props.