  We present 3.5cm and 6.2cm radio continuum maps in total and polarized
intensity of the barred galaxies NGC 1097 and NGC 1365. Both galaxies exhibit
radio ridges roughly overlapping with the massive dust lanes in the bar region.
The contrast in total intensity across the radio ridges is compatible with
compression and shear of an isotropic random magnetic field. The contrast in
polarized intensity is significantly smaller than that expected from
compression and shearing of the regular magnetic field; this could be the
result of decoupling of the regular field from the dense molecular clouds. The
regular field in the ridge is probably strong enough to reduce significantly
shear in the diffuse gas (to which it is coupled) and hence to reduce magnetic
field amplification by shearing. This contributes to the misalignment of the
observed field orientation with respect to the velocity vectors of the dense
gas. Our observations, for the first time, indicate that magnetic forces can
control the flow of the diffuse interstellar gas at kiloparsec scales. The
total radio intensity reaches its maximum in the circumnuclear starburst
regions, where the equipartition field strength is about 60\mu G, amongst the
strongest fields detected in spiral galaxies so far. The regular field in the
inner region has a spiral shape with large pitch angle, indicating the action
of a dynamo. Magnetic stress leads to mass inflow towards the centre,
sufficient to feed the active nucleus in NGC 1097. We detected diffuse X-ray
emission, possibly forming a halo of hot gas around NGC 1097.
