G32.4+0.1 is a Galactic supernova remnant (SNR) that belongs tothe class of SNRs that exhibit X-ray spectra that are dominated not bythermal emission but instead by synchrotron radiation. Prominent examples of SNRs in this class include SN 1006, G266.2-1.2 (Vela Jr.) and G347.3-0.5, and detailed studies of the synchrotron X-ray emission from these SNRs hold the promise of elucidating how these sources accelerate cosmic-ray electrons to extremely relativistic energies. Because only a few Galactic SNRs have been firmly established in the literature to belong to this class, detailed studies of each member are crucial. G32.4+0.1 — which is believed to lie at a distance exceeding 15 — is a heavily obscured object and for this reason it is one of the lesser-studied Galactic SNRs with synchrotron X-ray-dominated spectra.We present a new X-ray observation made with XMM-Newton of this SNR along with new L-band and P-band observations made with the JVLA. The purposes of these observations is to facilitate a detailed spatially-resolved spectroscopic X-ray analysis of the synchrotron emission from G32.4+0.1 along with clear measurements of the integrated flux densities of the SNR at these two radio frequencies and the corresponding spectral index of the SNR as well. Initial results will be presented and discussed.