An Earth-rotation aperture-synthesis technique was combined with the methods of interference polarimetry to study the total intensity and linear-polarization properties of the two radio sources 3C 10 and 3C 58 with a resolution of approximately 1 minute of arc at both 1420 and 2880 MHz These data were then used to calculate the distributions of spectral index, rotation measure, intrinsic position angle, and depolarization for the sources The source 3C 10 (Tycho's supernova, SN 1572) is thought to be the remnant of a Type I supernova 5000 pc distant and 120 pc above the galactic plane The total radiation has an annular structure with a sharp outer edge and with little emission from the central regions The polarized flux density has a similar, though less complete, ringlike shape Although the integrated emission shows litt1e polarization, many areas are polarized in excess of 5 percent at 21.1 cm and 10 percent at 10 4 cm The rotation measure ranges from -6 to +60 rad with no obvious positional organization The distribution of intrinsic position angles implies the existence of a radial component to the magnetic field. The depolarization distribution is seemingly random A search for relations among the various source parameters failed to reveal any strong correlations The source 3C 58, on the basis of the present work, is thought to be the remnant of a supernova 5000 pc distant and 270 pc above the galactic plane. In the total radiation it has a simple shape, brightest in the center and falling off slowly to zero at the edges, with an east-west elongation. The distribution of polarized emission is quite complex with some possibly unresolved regions. Although the source has little integrated polarization, when resolved, many regions exhibit polarizations exceeding 10 percent at 21.1 cm and 15 percent at 10.4 cm. The spectral index appears to be relatively flat in the central and south-central regions of the source and steeper toward the edges. The rotation measure changes smoothly from -67 rad in the eastern region to -125 rad in the western region. The distribution of intrinsic position angles implies an organized component of the magnetic field parallel to the major east-west axis over the full extent of the source. The depolarization distribution is seemingly random. Again, no strong correlations could be found between the various source parameters.