Drndic studied physics and mathematics at Harvard University and spent a year at the University of Cambridge in the Semiconductor Physics Group. At Cambridge Drndic worked on quantum transport of coupled gases with Michael Pepper. At Harvard University she was a member of Phi Beta Kappa and graduated summa cum laude. Drndic was awarded a Clare Booth Luce Fellowship, the Harold T. White Prize for Excellence in Teaching and the Robbins Prize from Harvard University. She remained there for her doctoral studies, working with Robert Westervelt on microelectromagnets for cold-atom experiments. She before joining the Massachusetts Institute of Technology as a Pappalardo Fellow. As a postdoctoral researcher Drndic worked on electron transport in cadmium selenide nanocrystals. She worked alongside Marc A. Kastner and Moungi Bawendi on novel spectroscopies.