A free-space method for the measurement of permittivity at millimetre wavelengths is described. This method utilizes the microwave analogue of the optical spectrometer, electromagnetic horns with lenses taking the place of the collimator and telescope of the optical instrument.At these wavelengths aperture dimensions are necessarily comparable with the radiated wavelength, and diffraction effects are pronounced. The design of the spectrometer and possible aperture illuminations are discussed using the concept of an angular spectrum of plane waves.Permittivities are measured using sheets of material on the spectrometer and studying the reflectivity with angle of incidence for different polarizations. Minima at which destructive interference occurs together with the Brewster angle are determined, and accurate values permittivity deduced.The effects of dielectric loss on the minima are investigated and are found to be small for normal values of loss tangent. The loss in the dielectric is assessed from the shape of the minima and by measurements of transmission coefficients. Diffraction effects on the measurement are discussed, whence it appears that the method should give identical results in both Fresnel and Fraunhofer regions of diffraction.Results for a whole range of specimen sizes and spacings in the instrument substantiate these conclusions, and show that the measurements of permittivity are accurate within ±0.5% in both regions of diffraction. An extension of the method to liquids is also described.