High-throughput methods for screening large populations of variant proteins are provided. The methods utilize large-scale arrays of microcapillaries, where 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 isolated, and cells expressing the variant proteins of interest can be characterized. Also provided are systems for performing the disclosed screening methods.