Single-cell genetic screens can be incredibly powerful, but current high-throughput platforms do not track dynamic processes, and even for non-dynamic properties they struggle to separate mutants of interest from phenotypic outliers of the wild-type population. Here we introduce SIFT, single-cell isolation following time-lapse imaging, to address these limitations. After imaging and tracking individual bacteria for tens of consecutive generations under tightly controlled growth conditions, cells of interest are isolated and propagated for downstream analysis, free of contamination and without genetic or physiological perturbations. This platform can characterize tens of thousands of cell lineages per day, making it possible to accurately screen complex phenotypes without the need for barcoding or genetic modifications. We applied SIFT to identify a set of ultraprecise synthetic gene oscillators, with circuit variants spanning a 30-fold range of average periods. This revealed novel design principles in synthetic biology and demonstrated the power of SIFT to reliably screen diverse dynamic phenotypes.