  Conjugations commuting with $\mathbf{M}_z$ and intertwining $\mathbf{M}_z$
and $\mathbf{M}_{\bar z}$ in $L^2(\mathcal{H})$, where $\mathcal{H}$ is a
Hilbert space, are characterized. We also investigate which of them leave
invariant the whole Hardy space $H^2(\mathcal{H})$ or a model space
$K_{\Theta}=H^2(\mathcal{H})\ominus\Theta H^2(\mathcal{H})$, where $\Theta$ is
a pure operator valued inner function.
