Supernova remnants (SNRs) have attracted a considerable amount of interest in modern astrophysics from both observational and theoretical perspectives. SNRs play an integral role in numerous processes associated with the evolution of galaxies, including the injection of significant amounts of kinetic energy and heavy-element–enriched material into the interstellar medium. In addition, SNRs have emerged as the leading candidates for the acceleration of cosmic rays within the disks of galaxies through the proposed diffusive shock acceleration (DSA) mechanism. Observations of SNRs have been conducted at three particular wavelengths, based on distinct processes of energy emission associated with these objects. Thermal bremsstrahlung emission from gas shock-heated to temperatures of 10–10 K, recombination radiation from ionized atomic species such as [S ii], and nonthermal synchrotron emission from relativistic electrons gyrating in the SNR’s magnetic field produce X-ray, optical, and radio emission, respectively. Studies of SNRs within our own Galaxy have been hampered by considerable distance uncertainties and massive extinction along Galactic lines of sight, particularly at the Xray and optical wavelengths. In contrast, the study of SNRs located in nearby galaxies—particularly galaxies located at high Galactic latitudes with face-on or nearly face-on orientations—offers the opportunity to examine equidistant samples of SNRs that are nearly free of obscuration. We present a multiwavelength (X-ray, optical, and radio) study of the resident SNR population of the Sculptor group galaxies NGC 300 and NGC 7793 and the northern granddesign spiral NGC 6946. These three galaxies are nearby (2.1, 3.38, and 5.1 Mpc distant, respectively), are located at high Galactic latitudes, and clearly exhibit extensive massive star formation throughout their disks. We have observed these galaxies at the wavelengths of 6 and 20 cm with the Very Large Array (VLA) and complemented this data with our own Ha images and archived X-ray observations made with the Position Sensitive Proportional Counter instrument aboard the ROSAT satellite. We have searched for X-ray and radio emission from previously known SNRs identified in the optical using the [S ii]/Ha method and searched for new candidate X-ray and radio SNRs. We have found that remarkably few of the optically identified SNRs possess counterparts at either of the other two wavelengths: of the 83 optically identified SNRs in these galaxies, only four (N300-S10, N300-S26, N7793-S26, and NGC 6946-S16) were also detected in the X-ray and the radio. N7793-S26 is a very noteworthy source: in the optical and radio it shows a remarkable filamentary structure approximately 450 pc in size, and its radio emission is nearly twice as luminous as the most radio luminous Galactic SNR, Cassiopeia A. Three other optically identified SNRs, N300-S11, N7793-S11, and NGC 6946-S9, feature strong radio emission but no X-ray emission. Our search for new SNRs in NGC 300 and NGC 7793 has produced 21 candidates: 14 candidate radio SNRs and two candidate X-ray SNRs in NGC 300, and five candidate radio SNRs in NGC 7793. Very limited intersection is seen between the sets of X-ray, optical, and radio-selected SNRs in these two galaxies. These results indicate possible selection effects inherent in these surveys: optical surveys favor the detection of SNRs in low-density regions that are relatively devoid of optical confusion. In contrast, radio and X-ray surveys are biased toward the detection of SNRs in high-density regions where optical surveys are severely impeded. Such selection effects may also indicate selection effects for the type of supernova that parents the SNR: the optical surveys are more likely to detect SNRs produced by the explosion of low-mass stars in Type Ia supernovae, while radio and X-ray surveys are more likely to identify SNRs produced by the explosion of high-mass stars in Type II supernovae. To investigate these selection effects, we have conducted a simulation designed to evaluate the dependence of optical detections of SNRs on distance to the target galaxy. By distributing artificial SNRs within the galaxy at positions corresponding to differing amounts of ambient density and varying the distance to the target galaxy, we find that the detection of SNRs using optical methods becomes increasingly difficult with distance and that SNRs that are embedded in regions of high density are not detected even when the galaxy is rather near. These results indicate the need for a multiwavelength campaign to detect a maximum number of SNRs in a galaxy of interest. A study of the average minimum energies of the radio SNRs in NGC 300, NGC 7793, NGC 6946, and the Local Group spiral M33 (which we have