  One-loop electroweak corrections to the annihilation cross-sections of dark
matter in the Higgs resonance region of the inert doublet model (IDM) are
investigated. The procedure of how to implement the width of the Higgs in order
to regularise the amplitude both at tree-level and at one-loop together with
the renormalisation of a key parameter of the model, are thoroughly
scrutinised. The discussions go beyond the application to the relic density
calculation and also beyond the IDM so that addressing these technical issues
can help in a wider context. We look in particular at the dominant channels
with the $b \bar b$ final state and the more involved 3-body final state, $W f
\bar f^\prime$, where both a resonance and an anti-resonance, due to
interference effects, are present. We also discuss how to integrate over such
configurations when converting the cross-sections into a calculation of the
relic density.
