We report observations with the MIPS instrument aboard the {it Spitzer Space Telescope} (SST) of four supernova remnants (SNRs) believed to be the result of core-collapse SNe: N132D (0525-69.6), N49B (0525-66.0), N23 (0506-68.0), and 0453-68.5. All four of these SNRs were detected in whole at 24 $mu$m and in part at 70 $mu$m. Comparisons with {it Chandra} broadband X-ray images show an association of infrared (IR) emission with the blast wave. We attribute the observed IR emission to dust that has been collisionally heated by electrons and ions in the hot, X-ray emitting plasma, with grain size distributions appropriate for the LMC and the destruction of small grains via sputtering by ions. As with our earlier analysis of Type Ia SNRs, models can reproduce observed 70/24 $mu$m ratios only if effects from sputtering are included, destroying small grains. We calculate the mass of dust swept up by the blast wave in these remnants, and we derive a dust-to-gas mass ratio of several times less than the often assumed value of 0.25% for the LMC. We believe that one explanation for this discrepancy could be porous (fluffy) dust grains.