The electrical and electromagnetic interference shielding (EMI) properties of composite materials made of polypropylene (PP) and carbon nanotubes (CNT) have been investigated in a broad frequency range, both experimentally and theoretically. A remarkably low percolation threshold of only 0.4 vol% and an exceptional shielding performance reaching effectiveness values as high as 90 dB are reported. The shielding effectiveness has been measured between 50 MHz and 18 GHz using two experimental methods (coaxial cell and wave guide cell) and the results were systematically correlated with the conductivity values of our composite materials. Furthermore, an EMI shielding theoretical model was developed and employed to predict the shielding properties of our PP/CNT composite materials as well as of numerous other composite materials reported in the literature and made by employing different polymer matrices and different types of fillers, of different nature (carbon black, carbon fibers, bamboo charcoal, mesoporous carbon, copper nanowires, reduced graphene oxide, etc). An excellent agreement is found between our theoretical calculations and the experimental data upon systematically varying the frequency of the incident wave, the fillers content and the sample thickness. Our model is allowing one thus to predictively design materials required to exhibit a specific value of EMI shielding effectiveness and operating in a specific frequency range. This can be of significant importance in numerous applications where shielding electromagnetic interference phenomena plays an important role.