  We study the collective magnetic excitations of the recently discovered
$C_{4}$ symmetric spin-density wave states of iron-based superconductors with
particular emphasis on their orbital character based on an itinerant
multiorbital approach. This is important since the $C_{4}$ symmetric
spin-density wave states exist only at moderate interaction strengths where
damping effects from a coupling to the continuum of particle-hole excitations
strongly modifies the shape of the excitation spectra compared to predictions
based on a local moment picture. We uncover a distinct orbital polarization
inherent to magnetic excitations in $C_{4}$ symmetric states, which provide a
route to identify the different commensurate magnetic states appearing in the
continuously updated phase diagram of the iron-pnictide family.
