Myriad biological functions require protein-protein interactions (PPIs), and engineered PPIs are crucial for applications ranging from drug design to synthetic cell circuits. Understanding and engineering specificity in PPIs is particularly challenging as subtle sequence changes can drastically alter specificity. Coiled-coils are small protein domains that have long served as a simple model for studying the sequence-determinants of specificity and have been used as modular building blocks to build large protein nanostructures and synthetic circuits. Despite their simple rules and long-time use, building large sets of well-behaved orthogonal pairs that can be used together is still challenging because predictions are often inaccurate, and, as the library size increases, it becomes difficult to test predictions at scale. To address these problems, we first developed a method called the Next-Generation Bacterial Two-Hybrid (NGB2H), which combines gene synthesis, a bacterial two-hybrid assay, and a high-throughput next-generation sequencing readout, allowing rapid exploration of interactions of programmed protein libraries in a quantitative and scalable way. After validating the NGB2H system on previously characterized libraries, we designed, built, and tested large sets of orthogonal synthetic coiled-coils. In an iterative set of experiments, we assayed more than 8,000 PPIs, used the dataset to train a novel linear model-based coiled-coil scoring algorithm, and then characterized nearly 18,000 interactions to identify the largest set of orthogonal PPIs to date with twenty-two on-target interactions.