  Top quark pair production in association with a $Z$-boson or a photon at the
LHC directly probes neutral top-quark couplings. We present predictions for
these two processes in the Standard Model (SM) Effective Field Theory (EFT) at
next-to-leading (NLO) order in QCD. We include the full set of CP-even
dimension-six operators that enter the top-quark interactions with the SM gauge
bosons. For comparison, we also present predictions in the SMEFT for top
loop-induced $HZ$ production at the LHC and for $t\bar{t}$ production at the
ILC at NLO in QCD. Results for total cross sections and differential
distributions are obtained and uncertainties coming from missing higher orders
in the strong coupling and in the EFT expansions are discussed. NLO results
matched to the parton shower are available, allowing for event generation to be
directly employed in an experimental analyses. Our framework provides a solid
basis for the interpretation of current and future measurements in the SMEFT,
with improved accuracy and precision.
