We study how nonstandard neutrino interactions (NSI) may be probed by a combination of coherent elastic neutrino-nucleus scattering, neutrino oscillation and collider data, from COHERENT, DUNE, T2HK and the high-luminosity (HL) LHC. We focus on NSI induced by a new flavored gauge boson Z in a generic anomaly-free ultraviolet-complete model. For Z masses above 10 GeV, the HL-LHC has the best sensitivity regardless of the flavor structure of the model. For masses between 0.01 GeV−10 GeV, current LHCb data and future COHERENT data have the best sensitivity unless the Z couplings to the first and second generation leptons are suppressed, in which case DUNE and T2HK have the best sensitivity. For Z masses between about 5 MeV−20 MeV, DUNE and T2HK have the best sensitivity. We also show how joint analyses of COHERENT and LHC data may constrain such models.