Planar cells provide an attractive alternative to traditional cylindrical cells for polymer electrolyte conductivity measurement as they not only allow sample quantity minimisation but also equilibration with vapour. They are also a key component in the parallel screening of combinatorially synthesised arrays of samples. A finite element simulation technique is used to calculate the complex cell constants of planar cells for a wide range of cell geometries. The real part and the phase of the cell impedance at the high frequency limit are identified as the most sensitive indicators of the polymer thickness, and thereby the cell constant, through which the measured impedance value yields the conductivity. Cell geometries are identified for which the conductivity may be determined in an optimally accurate fashion.