Among the more promising techniques for achieving fusion in the laboratory are those involving spherical or cylindrical implosions, such as Inertial Confinement Fusion or Z-pinch related concepts. In practice, these techniques tend to suffer from the disruptive effects of various problems, including in particular Richtmyer-Meshkov and Rayleigh-Taylor instabilities. Since the fluids involved are often plasmas and hence electrically conductive, there exists the possibility that an externally applied magnetic field may mitigate the effects of these factors. The work presented here considers computationally the potential to suppress some of these instabilities in cylindrical and spherical converging flows under the framework of ideal magnetohydrodynamics (MHD). The presentation will discuss effects of magnetic fields on the large-scale dynamics of flows such as these and on the instabilities themselves, under physically plausible field configurations with various symmetries. We find that these instabilities are indeed suppressed through the transport of baroclinic vorticity away from the perturbed density interface roughly along magnetic field lines. As a natural result, the quality and extent of suppression of the instabilities varies with local orientation of the magnetic field to the interface. The presence of the magnetic field however imposes asymmetry on the flow, depending on the particular strength and configuration of the field that is used. This symmetry-breaking effect may itself, among other effects, compromise the peak pressures attainable on convergence of the implosion, so that care should be taken in selection of the appropriate configuration and strength of the applied field.