The microwave conductivity and permittivity of both single-walled and multi-walled carbon nanotube (SWCNT and MWCNT) sponges were measured while compressing the samples. Compression leads to a huge variation of the absorptance, reflectance, and transmittance of the samples. The dependence of the microwave conductivity on the sponge density follows a power-law relation with exponents 1.7 ± 0.1 and 2.0 ± 0.2 for MWCNT and SWCNT sponges, respectively. These exponents can be decreased slightly by the addition of a non-conducting component which partly electrically separates adjacent tubes within the samples. The conductivity of MWCNT sponge was measured in the terahertz range while heating in air from 300 to 513 K and it increased due to an increase of a number of conducting channels in MWCNTs.