Co-evolution is a powerful problem-solving approach. However, fitness evaluation in co-evolutionary algorithms can be computationally expensive, as the quality of an individual in one population is defined by its interactions with many (or all) members of one or more other populations. To accelerate co-evolutionary systems, we introduce phylogenyinformed interaction estimation, which uses runtime phylogenetic analysis to estimate interaction outcomes between individuals based on how their relatives performed against each other. We test our interaction estimation method with three distinct co-evolutionary systems: two systems focused on measuring problem-solving success and one focused on measuring evolutionary open-endedness. We find that phylogeny-informed estimation can substantially reduce the computation required to solve problems, particularly at the beginning of long-term evolutionary runs. Additionally, we find that our estimation method initially jump-starts the evolution of neural complexity in our open-ended domain, but estimation-free systems eventually “catch-up” if given enough time. Further refinements to these phylogeny-informed interaction estimation methods offer a promising path to reducing the computational cost of running co-evolutionary systems while maintaining their open-endedness.