ABSTRACT Whilst intense solar flares are almost always accompanied by a coronal mass ejection (CME), reports on stellar CMEs are rare, despite the frequent detection of stellar ‘super flares’. The torus instability of magnetic flux ropes is believed to be one of the main driving mechanisms of solar CMEs. Suppression of the torus instability, due to a confining background coronal magnetic field that decreases sufficiently slowly with height, may contribute to the lack of stellar CME detection. Here, we use the solar magnetic field as a template to estimate the vertical extent of this ‘torus-stable zone’ (TSZ) above a stellar active region. For an idealized potential field model comprising the fields of a local bipole (mimicking a pair of starspots) and a global dipole, we show that the upper bound of the TSZ increases with the bipole size, the dipole strength, and the source surface radius where the coronal field becomes radial. The boundaries of the TSZ depend on the interplay between the spots’ and the dipole’s magnetic fields, which provide the local- and global-scale confinement, respectively. They range from about half the bipole size to a significant fraction of the stellar radius. For smaller spots and an intermediate dipole field, a secondary TSZ arises at a higher altitude, which may increase the likelihood of ‘failed eruptions’. Our results suggest that the low apparent CME occurrence rate on cool stars is, at least partially, due to the presence of extended TSZs.