The composites and thin films comprising individual single-walled carbon nanotubes with a polymer coating (p-CNTs) have been prepared and their electromagnetic responses have been studied in a wide range from low-frequency (25-107 Hz) up to the infrared region. In spite of the high volume fraction of the nanotubes (up to 3.3%), the polymer coating prevents direct p-CNT contacts and the formation of the percolation network in those composites, so that p-CNTs interact only via the electromagnetic coupling. Thereby it is an ideal model system to verify experimentally the fundamental issues related to carbon nanotube electromagnetics, such as the influence of inter-tube electron tunneling on the localized plasmon resonance in the terahertz range, or the infrared absorption enhancement of polymer molecules attached to the nanotube surface. Along with addressing the fundamentals, applied carbon nanotube electromagnetics got insights important for the applications of p-CNT based composites as dielectric media in the terahertz regime. In particular, we found that the real part of the permittivity of the p-CNT film in the terahertz range is rather competitive, i.e. 8-13, however the loss tangent is not so small (0.4-0.6) as has been predicted. The way to increase p-CNT terahertz performance is also discussed.