Similar to how it's done on some other sites (such as smashboards). Let a user sign in to their account and be able to claim some performance from a tournament as theirs and have it to show up under their "tournaments" tab.
ie. I participate in a tournament in person with no online setup, it's bracket gets set up in challonge (without using email addresses), allow me to tag a participant as "me" after the fact so it shows up in my tournament history. (To prevent fraud you could require that the tournament organizer approves each request.)