In this contribution, tracking control designs using output feedback are presented for a two-phase Stefan problem (SP) arising in the modeling of the vertical gradient freeze process. The two-phase SP, consisting of two coupled free boundary problems, is a vital part of many crystal growth processes due to the temporally varying spatial extent of the solid and liquid domains during growth. After discussing the special needs of the process, collocated and flatness-based state feedback designs are carried out. The quality of the provided approximations and the performance and robustness against parameter uncertainties of the open- and closed-loop control setups are analyzed in several simulations.