Ionic liquids are a relatively new class of materials with properties that make them attractive for a wide variety of engineering applications. For design purposes, it is useful to have a relatively simple model (i.e., excess Gibbs energy model or equation-of-state model) capable of describing the physical properties and equilibrium behavior of ILs and IL solutions. We consider here the performance of two selected models, NRTL applied to the modeling of liquid-liquid equilibrium and an electrolyte equation-of-state applied to the modeling of aqueous mean ionic activity coefficients. In each case we focus on issues in parameter estimation, and use an approach based on interval mathematics to solve the parameter estimation problem globally. Sample results are presented and suggest that the models considered here may be useful for correlation of data, but may not be well suited for prediction.