In general, the state of acting with honor--a quality often associated with Knights and Paladins.
Also, a Monster Trait from the Book of Engoku:
Players who are Honorable must accept a duel with the first enemy player who asks each battlegame. This duel is treated as an Honor Duel.
In theory, any player can roleplay this sort of effect, as well. However, non-Bushi will not automatically get an Honor Duel out of it. If you want to do this while playing something else, see if you can get a Bard or Wizard to supply the magic for you! Alternatively, the Reeve may grant it if asked nicely, or you can simply ask other players to respect your duel--they're not obligated to do so, but many courteous ones will still do so. Be sure to flurb it up!