Twitter provides a way for users to favorite tweets they like. This provides users a good way to reference tweets they want to read later or also look back and read those tweets again.
Just like backing up your tweets and Twitter profile, you can also also choose to backup your Twitter favorites and store it someplace safe. The Twitter favorite backup service is provided by Diigo, one of the companies I am coming to love for their products which include a note taking and sticky notes Chrome app for Google Chrome.
First off, you will require a new Diigo account to backup or save your Twitter favorites. Creating an account is simple, go ahead and register here. Once you have done that, log into Diigo and click on this link. On this page, you can now connect your Twitter account with Diigo and it will automatically save your twitter favorites to Diigo on a daily basis.
Once you have connected your accounts, you will be able to select whether you want to save all favorites or only favorites which contain links and whether those should be saved publicly or privately on Diigo. In addition to that Diigo will also convert those tweets into bookmarks or notes and can be organized using #hashtags.
P.S. You can also import your Delicious bookmarks to Diigo.