It is curious that Galadriel uses her mirror to test the only two members of the Company who will ever bear the Ring. Does this fall under her knowing ‘in part what also shall be’ (FR 2.vii.357)?
At the Ford of Bruinen Frodo defies the Ringwraiths' demand for the Ring, and attempts to command them to '[g]o back to the Land of Mordor, and follow me no more!' (FR 1.xii.215). In response they laugh at him and tell him that they will take him to Mordor. In The Mirror of Galadriel Frodo offers to give Galadriel the Ring. In response she, too, laughs, but clearly at herself and her situation, and tells him that it is time for him to leave Lothlórien (FR 1.vii.365-366).