One hallmark of natural organisms is their significant evolvability, i.e.,their increased potential for further evolution. However, reproducing such evolvability in artificial evolution remains a challenge, which both reduces the performance of evolutionary algorithms and inhibits the study of evolvable digital phenotypes. Although some types of selection in evolutionary computation indirectly encourage evolvability, one unexplored possibility is to directly select for evolvability. To do so, we estimate an individual's future potential for diversity by calculating the behavioral diversity of its immediate offspring, and select organisms with increased offspring variation. While the technique is computationally expensive, we hypothesized that direct selection would better encourage evolvability than indirect methods. Experiments in two evolutionary robotics domains confirm this hypothesis: in both domains, such Evolvability Search produces solutions with higher evolvability than those produced with Novelty Search or traditional objective-based search algorithms. Further experiments demonstrate that the higher evolvability produced by Evolvability Search in a training environment also generalizes, producing higher evolvability in a new test environment without further selection. Overall, Evolvability Search enables generating evolvability more easily and directly, facilitating its study and understanding, and may inspire future practical algorithms that increase evolvability without significant computational overhead.