A new method to characterize microwave electromagnetic (EM) absorption of a bulk carbon nanotube (CNT) material is proposed and experimentally evaluated in this paper. The method is based on the measurement of microwave transmission through a capacitive-resonator aperture (CRA) in a conductive screen loaded with a CNT sample under test. This method allows us to measure microwave permittivity and absorption of thin samples (∼0.1 μm–10 μm thick) with linear dimensions much smaller than the wavelength of radiation in free space. This “minimal” sample requirement restricts the application of conventional microwave characterization methods such as free-space or waveguide permittivity characterization. It is demonstrated that the resonance E-field enhancement inside the CRA leads to strong EM interaction of the microwave E-field with the CNT sample under test, thus enabling high sensitivity and dynamic range (∼5 dB) of the measurement procedure. Another advantage of the proposed technique over conventional non-resonance characterization methods is that in the resonance transmission band, the CRA operation is reflection-less, which leads to a relatively simple qualitative algebraic de-embedding procedure of the material parameters based on the principle of energy conservation. The experimental microwave absorption data of the multiwall CNT samples are presented in the S frequency band (2–4 GHz), demonstrating microwave absorption properties of the multiwall CNT ribbons.