Two relevant computational models, one relying on a Level-Set approach, the other one on a Volume-of-Fluid tracking procedure with piecewise linear interface reconstruction, are comparatively assessed in terms of their capability to simulate crystallization of supercooled water. The models are preliminary validated by computing a one-dimensional freezing front propagation for which an analytic solution exists. Afterwards, the tip velocity of two-dimensional dendrites growing in supercooled water is determined and compared with corresponding experimental results and theoretical predictions in the range of supercooling between 1 K and 30 K. Present modeling results following closely both the underlying theory and experimental findings show very good mutual agreement.