  We study $W^+W^-$ and $Zh$ final states at future linear $e^+e^-$ colliders;
designing analyses specific to the various final state polarizations allows us
to target specific beyond the Standard Model (BSM) effects, parametrized in the
form of dimension-6 operators. We find that CLIC can access effects roughly an
order of magnitude smaller than HL-LHC or ILC, and two orders of magnitude
smaller than LEP. These results are interpreted in the context of
well-motivated BSM scenarios---at weak and strong coupling---where we expect
correlated effects in Drell-Yann processes. The latter turn out to have better
discovery potential, although the diboson processes provide additional
discriminating power, potentially furnishing a way to measure the spin and
coupling of BSM states.
