This paper is devoted to the influence of the multi-walled carbon nanotube (MWCNT) spatial distribution within a polymer matrix on the electrophysical properties of the composite. We have studied composites with MWCNT concentrations close to the percolation threshold upon variation in (i) the morphology of the reinforcing material using MWCNTs with different aspect ratio and nanotube aggregate size (up to the average size of ≈300 µm) that were isolated from each other by thin polymer layers, and (ii) the type of the polymer matrix. The composites obtained have been characterized using optical and scanning electron microscopy, and DC conductivity measurements. A study of the electromagnetic response in microwave (0.01–18 GHz) and terahertz (100–200 GHz) ranges was performed. In the region close to and above the percolation threshold, the electrophysical properties of the composites were found to be strongly affected by the spatial distribution of MWCNTs in the composite matrix. The effect of conductive fillers (NTs) size on the EMI reflectance of the composites was different for microwave and terahertz ranges.