  We present results from a complete next-to-leading order (NLO) calculation of
$e^+e^-\rightarrow ZH$ in the Standard Model Effective Field Theory (SMEFT)
framework, including all contributions from dimension-6 operators. At NLO,
there are novel dependencies on CP violating parameters in the gauge sector, on
modifications to the Higgs boson self-couplings, on alterations to the top
quark Yukawa couplings, and on 4-fermion operators involving the electron and
the top quark, among others. We show that including only the logarithms
resulting from renormalization group scaling can produce misleading results,
and further, we explicitly demonstrate the constraining power of combining
measurements from different energy scales.
