  We explore the indirect sensitivities to decoupled new physics of prospective
precision electroweak measurements, triple-gauge-coupling measurements and
Higgs physics at future $e^+e^-$ colliders, with emphasis on the ILC250 and
FCC-ee. The Standard Model effective field theory (SM EFT) is adopted as a
model-independent approach for relating experimental precision projections to
the scale of new physics, and we present prospective constraints on the Wilson
coefficients of dimension-6 operators. We find that in a marginalised fit
ILC250 EWPT measurements may be sensitive to new physics scales $\Lambda =
\mathcal{O}(10)$~TeV, and FCC-ee EWPT measurements may be sensitive to $\Lambda
= \mathcal{O}(30)$~TeV. The prospective sensitivities of Higgs and TGC
measurements at the ILC250 (FCC-ee) are to $\Lambda = \mathcal{O}(1)$~TeV
($\Lambda = \mathcal{O}(2)$~TeV).
