  Gamma-ray lines from dark matter annihilation ($\chi\chi\to \gamma X$, where
$X=\gamma,h,Z$) are always accompanied, at lower energies, by a continuum
gamma-ray spectrum stemming both from radiative corrections ($X=\gamma$) and
from the decay debris of the second particle possibly present in the final
state ($X=h,Z$). This model-independent gamma-ray emission can be exploited to
derive novel limits on gamma-ray lines that do not rely on the line-feature.
Although such limits are not expected to be as stringent, they can be used to
probe the existence of $\gamma$-ray lines for dark matter masses beyond the
largest energies accessible to current telescopes. Here, we use continuous
gamma-ray searches from Fermi-LAT observations of Milky Way dwarf spheroidal
galaxies and from H.E.S.S. observations of the Galactic Halo to extend the
limits on the annihilation cross sections into monochromatic photons to dark
matter masses well beyond $500$ GeV (Fermi-LAT) and $20$ TeV (H.E.S.S.). In
this large mass regime, our results provide the first constraints on
$\gamma$-ray lines from dark matter annihilation.
