Multi-stage sample-recovery systems, including automated 2-stage and 3-stage sample-recovery systems, are provided. Such systems enable the rapid screening and recovery of samples, including viable cell-based samples, from high-throughput screening systems, including systems utilizing large-scale arrays of microcapillaries. In specific screening systems, each microcapillary comprises a solution containing a variant protein, an immobilized target molecule, and a reporter element. Immobilized target molecules may include any molecule of interest, including proteins, nucleic acids, carbohydrates, and other biomolecules. The association of a variant protein with a molecular target is assessed by measuring a signal from the reporter element. The contents of microcapillaries identified in the assays as containing variant proteins of interest can be identified and recovered using the multi-stage systems disclosed herein.