  We study Higgs boson production in exclusive jet bins at possible future 33
and 100 TeV proton-proton colliders. We compare the cross sections obtained
using fixed-order perturbation theory with those obtained by also resuming
large logarithms induced by the jet-binning in the gluon-fusion and associated
production channels. The central values obtained by the best-available
fixed-order predictions differ by $10-20\%$ from those obtained after including
resummation over the majority of phase-space regions considered. Additionally,
including the resummation dramatically reduces the residual scale variation in
these regions, often by a factor of two or more. We further show that in
several new kinematic regimes that can be explored at these high-energy
machines, the inclusion of resummation improvement is mandatory.
