The influence of a transverse magnetic field on the formation and evolution of supersonic plasma jets and shocks was studied experimentally, and compared with 3D numerical simulations. An improved jet collimation was seen due to the change in the magnetic field topology restricting the radial expansion of the ablated plasma. The magnetic field was also shown to strongly affect the shock structures, both indirectly through the modified jet geometry, as well as due to a compression of the field lines in the shock region. The interaction characteristics were found to depend on the relative contribution of the magnetic and plasma pressure in balancing the ram pressure of the jet.