Computer-aided molecular design (CAMD) methods can be used to generate promising solvents with enhanced reaction kinetics, given a reliable model of solvent effects on reaction rates. Herein, we use a surrogate model parameterised from computer experiments, more specifically, quantum-mechanical (QM) data on rate constants. The choice of solvents in which these computer experiments are performed is critical, considering the cost and difficulty of these QM calculations. We investigate the use of model-based design of experiments (MBDoE) to identify an information-rich solvent set and integrate this within a QM-CAMD framework. We find it beneficial to consider a wide range of solvents in designing the solvent set, using group contribution techniques to predict missing solvent properties. We demonstrate, via three case studies, that the use of MBDoE yields surrogate models with good statistics and leads to the identification of solvents with enhanced predicted performance with few iterations and at low computational cost.