  We present results from a set of numerical simulations aimed at exploring the
mechanism of coronal mass ejection (CME) suppression in active stars by an
overlying large-scale magnetic field. We use a state-of-the-art 3D
magnetohydrodynamic (MHD) code which considers a self-consistent coupling
between an Alfv\'en wave-driven stellar wind solution, and a first-principles
CME model based on the eruption of a flux-rope anchored to a mixed polarity
region. By replicating the driving conditions used in simulations of strong
solar CMEs, we show that a large-scale dipolar magnetic field of $75$ G is able
to fully confine eruptions within the stellar corona. Our simulations also
consider CMEs exceeding the magnetic energy used in solar studies, which are
able to escape the large-scale magnetic field confinement. The analysis
includes a qualitative and quantitative description of the simulated CMEs and
their dynamics, which reveals a drastic reduction of the radial speed caused by
the overlying magnetic field. With the aid of recent observational studies, we
place our numerical results in the context of solar and stellar flaring events.
In this way, we find that this particular large-scale magnetic field
configuration establishes a suppression threshold around $\sim$$3 \times
10^{32}$~erg in the CME kinetic energy. Extending the solar flare-CME relations
to other stars, such CME kinetic energies could be typically achieved during
erupting flaring events with total energies larger than $6 \times 10^{32}$ erg
(GOES class $\sim$X70).
