We investigate, for two water models displaying a liquid-liquid critical point, the relation between changes in dynamic and ther-modynamic anomalies arising from the presence of the liquid-liquid critical point. We find a correlation between the dynamic crossover and the locus of specific heat maxima$C_{P}^{max}$("Widom line") emanating from the critical point. Our findings are consistent with a possible relation between the previously hypothesized liquid-liquid phase transition and the transition in the dynamics recently observed in neutron scattering experiments on confined water. More generally, we argue that this connection between$C_{P}^{max}$and dynamic crossover is not limited to the case of water, a hydrogen bond network-forming liquid, but is a more general feature of crossing the Widom line. Specifically, we also study the Jagla potential, a spherically symmetric two-scale potential known to possess a liquid-liquid critical point, in which the competition between two liquid structures is generated by repulsive and attractive ramp interactions.