Tuning an algorithm requires to evaluate it under different configurations on several problem instances. Such evaluations are costly. A way to reduce the configuration time when developing tuners is to use surrogate models, which map configuration-instance pairs to the approximate algorithm performance and thus allow to replace algorithm runs by fast calls to the model. Most applications of surrogate models found in the literature focus on predicting algorithm running time; much less effort has been devoted to predicting the quality of solutions of optimization algorithms. In this paper, we present a comparative study of surrogate models for predicting solution quality. We evaluate several surrogate models from the literature, including random forests, gradient boosting methods, and neural networks, and compare ways of handling different classes of parameters, data imputation strategies, and codification of instances. We demonstrate for two heuristic algorithms that the best models can accurately reproduce effects observed when tuning with the ground truth. Our code is available ( https://github.com/gutodelazeri/oracle ).