Matching NLL to NLO in Higgs and Z plus jet at the LHC and FCC

We present updated predictions for rapidity and transverse-momentum spectra in Higgs-plus-jet production at proton colliders, combining NLO fixed-order QCD with next-to-leading energy-logarithmic resummation. Preliminary results for the $Z$-boson case are also discussed. Our study underscores the importance of improving fixed-order predictions for Higgs- and $Z$-plus-jet observables to meet the precision demands of Higgs and electroweak measurements at the LHC and future FCC energies.