  Effective Lagrangians are a useful tool for a data-driven approach to physics
beyond the Standard Model at the LHC. However, for the new physics scales
accessible at the LHC, the effective operator expansion is only relatively
slowly converging at best. For tree-level processes, it has been found that the
agreement between the effective Lagrangian and a range of UV-complete models
depends sensitively on the appropriate definition of the matching. We extend
this analysis to the one-loop level, which is relevant for electroweak
precision data and Higgs decay to photons. We show that near the scale of
electroweak symmetry breaking the validity of the effective theory description
can be systematically improved through an appropriate matching procedure. In
particular, we find a significant increase in accuracy when including suitable
terms suppressed by the Higgs vacuum expectation value in the matching.
