We investigate the behaviour of the ideal magnetohydrody-namic (MHD) Richtmyer-Meshkov instability (RMI) in two-dimensional implosions under the influence of uniform- and saddle-topology seed magnetic fields. The RMI is a hydrody-namic instability that, along with the Rayleigh-Taylor instability, greatly limits the operating parameters of inertial confinement fusion (ICF), a technology that has recently seen much interest for its potential for energy production. The instability arises when a perturbed density interface is impulsively accelerated, for example by a shock wave, causing the perturbations on the interface to grow as a result of baroclinic vorticity generation. Here we present case studies of the MHD RMI in converging two-dimensional geometry, in the presence of uniform- and saddle-topology seed fields. We examine the shock refraction process, identifying the waves that result from it, and determine the growth rate of the RMI, comparing it to its behaviour in the converging hydrodynamic (no-field) case. We drive the incident shocks with a Riemann problem, and examine the RMI under various perturbation wavenumbers and seed field strengths. The shock refraction processes produce a collection of fast and sub-fast MHD shock waves which carry vorticity along and away from the interface perturbations, depending on the local field orientation to the interface, supressing the instability but leading to slightly irregular perturbation shapes. These results encourage further research on the MHD RMI in converging flows, with a strong potential for application to ICF experiments.