• Extend optimal experimental design for guaranteed parameter estimation to LLE systems • Employ rigorous calculations for the LLE using the Baker’s criterion • Avoid problematic parameter values, which may lead to erroneous predictions • Present proof-of-concept case study, reducing the parameter uncertainty by at least 10.3924909 % Semi-empirical models for LLE are essential for chemical process design but rely on experimental data for parameter estimation. In the face of high experimental costs, determining an informative experimental plan is crucial for constructing and validating these models efficiently. OED for (bounded-error) guaranteed GPE is a valuable approach to planning LLE experiments, but it has been limited to systems with simple input-output relations. We extend this method to systems whose input-output relation is implicitly given by an equation system with additional semi-infinite constraints, which corresponds to the rigorous computation of an LLE. Excess Gibbs free energy models are highly flexible but can predict spurious phase splits due to (i) using non-rigorous computations, or (ii) parameter values that are problematic in the sense that they lead to erroneous model behavior. To mitigate these issues in experiment planning, we (i) employ rigorous calculations using Baker’s criterion, and (ii) enforce additional requirements, based on [Mitsos et al. Chem. Eng. Sci., 64(3):548–559, 2009] to exclude parameter values that lead to erroneous model behavior. We solve the resulting problem using (generalized) semi-infinite programming techniques and provide a proof of concept using the Redlich-Kister model to plan the OED to reduce parameter uncertainty. Our approach successfully avoids wrong predictions due to problematic parameter values and computes an experimental design that significantly reduces the predicted parameter uncertainty. However, our method is computationally demanding, necessitating advancements in numerical methods for practical applications involving multiple parameters or more complex excess models.