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Measuring the DC conductivity of very thin films could be rather difficult because of the electrical contact issue. This DC conductivity can, however, be extracted from noncontact measurements at GHz and THz frequencies using elaborated conductivity models that nicely fit the experimental data. Here we employ this technique to study the DC conductivity of fragile nanometer-thick films of multiwalled carbon nanotubes and monolayer graphene. The THz response of the films is measured by THz time-domain spectroscopy. We show that the THz conductivity of the samples is well fitted by either Drude-Lorentz model or Drude-Smith model, giving information on the physics of electrical conductivity in these materials. This extraction procedure is validated by the good agreement between the so-obtained DC conductivity and the one measured with a classical 4-point probe in-line contact method.