Recent studies have highlighted the promise of targeting tumor neoantigens to generate potent antitumor immune responses and provide strong motivation for improving our understanding of antigen-T-cell receptor (TCR) interactions. Advances in single-cell sequencing technologies have opened the door for detailed investigation of the TCR repertoire, providing paired information from TCRα and TCRβ, which together determine specificity. However, a need remains for efficient methods to assess the specificity of discovered TCRs. We developed a streamlined approach for matching TCR sequences with cognate antigen through on-demand cloning and expression of TCRs and screening against candidate antigens. Here, we first demonstrate the system’s capacity to identify viral-antigen-specific TCRs and compare the functional avidity of TCRs specific for a given antigen target. We then apply this system to identify neoantigen-specific TCR sequences from patients with melanoma treated with personalized neoantigen vaccines and characterize functional avidity of neoantigen-specific TCRs. Furthermore, we use a neoantigen-prediction pipeline to show that an insertion-deletion mutation in a putative chronic lymphocytic leukemia (CLL) driver gives rise to an immunogenic neoantigen mut-MGA, and use this approach to identify the mut-MGA-specific TCR sequence. This approach provides a means to identify and express TCRs, and then rapidly assess antigen specificity and functional avidity of a reconstructed TCR, which can be applied for monitoring antigen-specific T-cell responses, and potentially for guiding the design of effective T-cell-based immunotherapies.