An innovative measurement setup for the dielectric characterisation of fibres in a terahertz time-domain spectrometer using an HDPE elliptical lens for coupling into the fibres has been built and validated by measurements of several different types of samples. The setup is based on a commercial all fibre-coupled terahertz time-domain spectrometer. Measurements of the effective refractive index have been conducted on polypropylene-based three-dimensional printing filaments, silica glass rods, and a polytetrafluoroethylene cord of lowered density, covering the frequency range of approximately 100 GHz to 1 THz. The theoretical part of the work includes numerical calculations performed via the finite difference eigenmode method and the characteristic equations of a uniform circular dielectric waveguide for a few guided modes, from which it is clear that primarily the fundamental mode propagates along the fibre. Details on model-based phase corrections, crucial to the accurate determination of the effective refractive index of dispersive fibres, have been presented as well.