We present multi-dimensional simulations of magnetized radiative jets appropriate to Young Stellar Objects . Magnetized jets subject to collisionally excited radiative losses have not , as yet , received extensive scrutiny . The purpose of this letter is to articulate the propagation dynamics of radiative MHD jets in the context of the extensive jet literature . Most importantly , we look for morphological and kinematic diagnostics that may distinguish hydrodynamic protostellar jets from their magnetically dominated cousins . Our simulations are axisymmetric ( 2 { 1 \over 2 } -D ) . A toroidal ( B _ { \phi } ) field geometry is used . Our models have high sonic Mach numbers ( M _ { s } \approx 10 ) , but lower fast mode Mach number ( M _ { f } \approx 5 ) . This is approximately the case for jets formed via disk-wind or X-wind models - currently the consensus choice for launching and collimating YSO jets . Time-dependent radiative losses are included via a coronal cooling curve . Our results demonstrate that the morphology and propagation characteristics of strongly magnetized radiative jets can differ significantly from jets with weak fields . In particular the formation of nose-cones via post-shock hoop stresses leads to narrow bow shocks and enhanced bow shock speeds . In addition , the hoop stresses produce strong shocks in the jet beam which constrasts with the relatively unperturbed beam in radiative hydrodynamic jets . Our simulations show that pinch modes produced by magnetic tension can strongly effect magnetized protostellar jets . These differences may be useful in observational studies designed to distinguish between competing jet collimation scenarios .