We show how leading radiative corrections can be implemented in the general description of $$h\rightarrow 4\ell $$ h → 4 ℓ decays by means of pseudo observables (PO). With the inclusion of such corrections, the PO description of $$h\rightarrow 4\ell $$ h → 4 ℓ decays can be matched to next-to-leading-order electroweak calculations both within and beyond the Standard Model (SM). In particular, we demonstrate that with the inclusion of such corrections the complete next-to-leading-order SM prediction for the $$h\rightarrow 2e2\mu $$ h → 2 e 2 μ dilepton mass spectrum is recovered within $$1\,\%$$ 1 % accuracy. The impact of radiative corrections for non-standard PO is also briefly discussed.