The complex dielectric constants of three polypropylene (PP) composite samples were measured at microwave frequency ranges of X (8.2-12.4 GHz) and Ka band (26.5-40 GHz), and as a function of filler content. Three types of carbon filler materials -- pristine multiwall carbon nanotubes (p-CNTs), functionalized multiwall carbon nanotubes (f-CNTs), and carbon black (p-CB) were investigated. Attenuation constant for each composite was calculated, based on its measured complex dielectric constant, to highlight the importance of studying frequency dependent performance of composite materials for microwave heating. Most of the reported works for polymer composite heating using microwave power, have been conducted using commercial microwave ovens operating at 2.45 GHz. The results of this investigation for the CNT-composite samples indicate the importance of frequency optimization for creating maximum heat generation. The composite samples were also irradiated using low-power microwave energy at 2.6, 10 and 28 GHz and using a thermographic camera their relative capabilities for producing heat was investigated. The heating results corroborated those of the dielectric property measurements.