  Higgs sector extensions beyond the Standard Model (BSM) provide additional
sources of CP violation and further scalar states that help to trigger a strong
first order electroweak phase transition (SFOEWPT) required to generate the
observed baryon asymmetry of the Universe through electroweak baryogenesis. We
investigate the CP-violating 2-Higgs-Doublet Model (C2HDM) and the
Next-to-Minimal 2-Higgs-Doublet Model (N2HDM) with respect to their potential
to generate an SFOEWPT while being compatible with all relevant and recent
theoretical and experimental constraints. The implications of an SFOEWPT on the
collider phenomenology of the two models are analysed in detail in particular
with respect to Higgs pair production. We provide benchmark points for
parameter points that are compatible with an SFOEWPT and provide distinct
di-Higgs signatures.
