Nearfield terahertz spectroscopy can be used to probe the terahertz conductivity of individual resonant particles. We applied this technique to individual microsized carbon fibres and observed strong plasmonic resonances in the terahertz range. Analysing the resonance frequency of the samples and the degree of field enhancement induced by the incident terahertz pulse, we estimated their terahertz conductivity (1-5.10⁴ S/m). This method can be useful for characterising semimetallic and semiconductor terahertz absorbers, microantennas and metamaterial elements.