The effect of the residual catalyst for the synthesis of multi-walled carbon nanotubes (MWCNTs) on the electrophysical properties of MWCNT–polyethylene composites produced by melt mechanical mixing was studied. The residual catalyst content was varied by changing the MWCNTs synthesis time. The nanotubes used in the work were characterized using transmission and scanning electron microscopy, atomic emission analysis, X-ray phase analysis, and magnetic permeability measurements. The structure of the synthesized composites was studied using optical and scanning electron microscopy. The dependences of the specific magnetization on the applied magnetic field, bulk electrical conductivity on the volumetric content of the filler in the composite, and the frequency dependences of the reflection, transmission, and absorption of electromagnetic radiation in the range 0.01–18 GHz were obtained. It was established that the obtained composites are characterized by a uniform distribution of nanotubes in the polymer matrix, and the dependence of the bulk electrical conductivity on the content of MWCNTs in the composite has a percolation character. Variation in the synthesis time of nanotubes allows producing MWCNTs with a high content of ferromagnetic particles, which are an alloy close in stoichiometry to the composition of the active component of the catalyst. It was shown that the use of composites modified with MWCNTs with a high content of residual catalyst is more effective for absorbing electromagnetic radiation due to an increase in their magnetic losses.