Designing enzymes to function in novel chemical environments is a central goal of synthetic biology with broad applications. Guiding protein design with machine learning (ML) has the potential to accelerate the discovery of high-performance enzymes by precisely navigating a rugged fitness landscape. In this work, we describe an ML-guided campaign to engineer the nuclease NucB, an enzyme with applications in the treatment of chronic wounds due to its ability to degrade biofilms. In a multi-round enzyme evolution campaign, we combined ultra-high-throughput functional screening with ML and compared to parallelin-vitrodirected evolution (DE) andin-silicohit recombination (HR) strategies that used the same microfluidic screening platform. The ML-guided campaign discovered hundreds of highly-active variants with up to 19-fold nuclease activity improvement, while the best variant found by DE had 12-fold improvement. Further, the ML-designed hits were up to 15 mutations away from the NucB wildtype, far outperforming the HR approach in both hit rate and diversity. We also show that models trained on evolutionary data alone, without access to any experimental data, can design functional variants at a significantly higher rate than a traditional approach to initial library generation. To drive future progress in ML-guided design, we curate a dataset of 55K diverse variants, one of the most extensive genotype-phenotype enzyme activity landscapes to date. Data and code is available at:https://github.com/google-deepmind/nuclease_design.