We present a study on the effects of the intracluster medium (ICM) on the interstellar medium (ISM) of 10 Virgo Cluster galaxies using Spitzer far-infrared (FIR) and Very Large Array radio continuum imaging. Relying on the FIR-radio correlation within normal galaxies, we use our infrared data to create model radio maps, which we compare to the observed radio images. For six of our sample galaxies, we find regions along their outer edges that are highly deficient in the radio compared with our models. We also detect FIR emission slightly beyond the observed radio disk along these outer edges. We believe these observations are the signatures of ICM ram pressure. For NGC 4522, we find the radio-deficit region to lie just exterior to a region of high radio polarization and flat radio spectral index, although the total 20 cm radio continuum in this region does not appear strongly enhanced. These characteristics seem consistent for other galaxies with radio polarization data in the literature. The strength of the radio deficit is inversely correlated with the time since peak pressure as inferred from stellar population studies and gas-stripping simulations, consistent with the strength of the radio deficit being a good indicator of the strength of the current ram pressure. We also find that galaxies having local radio deficits appear to have enhanced global radio fluxes. Our preferred physical picture is that the observed radio-deficit regions arise from the ICM wind sweeping away cosmic-ray (CR) electrons and the associated magnetic field, thereby creating synchrotron tails as observed for some of our galaxies. We propose that CR particles are also reaccelerated by ICM-driven shocklets behind the observed radio-deficit regions which, in turn, enhances the remaining radio disk brightness. The high radio polarization and lack of precisely coincident enhancement in the total synchrotron power for these regions suggest shearing, and possibly mild compression of the magnetic field, as the ICM wind drags and stretches the leading edge of the ISM.