Supercooled water has been the subject of numerous studies by researchers trying to understand the unusual properties of water, which are pronounced in the supercooled state. The thermodynamic phenomena underlying the observed anomalies of water, and their relation to the microscopic properties of the liquid have not been fully understood. Lattice models offer a way of establishing such relationships. We present results from studies of two related models that exhibit qualitative behavior similar to water. The results suggest a range of metastable phase behaviors which are qualitatively consistent with the equilibrium behavior of water.