  We describe a number of improvements to the GENEVA method for matching NNLO
calculations to parton shower programs. In particular, we detail changes to the
resummed calculation used in the matching procedure, including disentangling
the cross section dependence on factorisation and beam scales, and an improved
treatment of timelike logarithms. We also discuss modifications in the
implementation of the splitting functions which serve to make the resummed
calculation differential in the higher multiplicity phase space. These changes
improve the stability of the numerical cancellation of the nonsingular term at
small values of the resolution parameter. As a case study, we consider the
gluon-initiated Higgs boson production process $gg\to H$. We validate the NNLO
accuracy of our predictions against independent calculations, and compare our
showered and hadronised results with recent data taken at the ATLAS and CMS
experiments in the diphoton decay channel, finding good agreement.
