This magnetic compression of cylindrical liners filled with DT gas has promise as an efficient way to achieve fusion burn using pulsed-power machines. However, to avoid rapid cooling of the fuel by transfer of heat to the liner an axial magnetic field is required. This field has to be compressed during the implosion since the thermal insulation is more demanding as the compressed DT plasma becomes hotter and its volume smaller. This compression of the magnetic field is driven both by the imploding liner and plasma. To highlight how this magnetic field compression by the plasma and liner evolves we have separately studied Z-pinch implosions generated by gas puff and liner loads. The masses of the gas puff and liner loads were adjusted to match COBRA's current rise times. Our results have shown that Ne gas-puff implosions are well described by a snowplow model where electrical currents are predominately localized to the outer surface of the imploding plasma and the magnetic field is external to the imploding plasma. Liner implosions are dominated by the plasma ablation process on the inside surface of the liner and the electrical currents and magnetic fields are advected into the inner plasma volume; the sharp radial gradient associated with the snowplow process is not present.