Gene-regulatory networks are ubiquitous in nature and critical for bottom-up engineering of synthetic networks. Transcriptional repression is a fundamental function that can be tuned at the level of DNA, protein, and cooperative protein-protein interactions, necessitating high-throughput experimental approaches for in-depth characterization. Here, we used a cell-free system in combination with a high-throughput microfluidic device to comprehensively study the different tuning mechanisms of a synthetic zinc-finger repressor library, whose affinity and co-operativity can be rationally engineered. The device is integrated into a comprehensive workflow that includes determination of transcription-factor binding-energy landscapes and mechanistic modeling, enabling us to generate a library of well-characterized synthetic transcription factors and corresponding promoters, which we then used to build gene-regulatory networks de novo. The well-characterized synthetic parts and insights gained should be useful for rationally engineering gene-regulatory networks and for studying the biophysics of transcriptional regulation.