Impedance techniques using circular microelectrodes are introduced in order to locally measure grain boundary properties in polycrystalline materials with highly conductive as well as highly resistive grain boundaries. Finite element calculations allow for a discussion of the general aspects, potentials and limits of such measurements and enable a quantitative analysis of local properties. The applicability of the methods are shown by detecting and analyzing highly conductive grain boundaries in AgCl and by locally measuring impedance spectra of highly resistive grain boundaries in acceptor-doped SrTiO3.