Dielectric waveguides are an emerging platform for terahertz (THz) integrated circuits, but a key challenge for dense integration is the realization of terminations that enable both multi-port device characterization and elimination of electromagnetic interference. Here, we demonstrate a compact, broadband termination by coating silicon waveguides with ultrathin single-walled carbon nanotube (SWCNT) films. Fabricated via a floating-catalyst (aerosol) chemical vapor deposition process, film thicknesses vary from 2 to 53 nm and are characterized in 140-220 GHz. A 53 nm thick film introduces up to 47 dB of attenuation while maintaining over 20 dB reflection loss, confirming nearly reflection-free absorption. Shielding analysis shows absorption dominates over reflection, and a record specific shielding efficiency of 5.5 x 109 dB cm2 g-1 is achieved. This approach offers a footprint-efficient solution for high-density THz circuits without bulky, radiative terminations.