  We study for the first time the collider reach on the derivative Higgs
portal, the leading effective interaction that couples a pseudo Nambu-Goldstone
boson (pNGB) scalar Dark Matter to the Standard Model. We focus on Dark Matter
pair production through an off-shell Higgs boson, which is analyzed in the
vector boson fusion channel. A variety of future high-energy lepton colliders
as well as hadron colliders are considered, including CLIC, a muon collider,
the High-Luminosity and High-Energy versions of the LHC, and FCC-hh.
Implications on the parameter space of pNGB Dark Matter are discussed. In
addition, we give improved and extended results for the collider reach on the
marginal Higgs portal, under the assumption that the new scalars escape the
detector, as motivated by a variety of beyond the Standard Model scenarios.
