This data set includes broadband (1e-4 to 1e5 Hz) frequency-dependent, complex electrical conductivity data, which have been measured in the laboratory by means of the spectral induced polarization (SIP) method on 28 oriented black shale and mudstone samples. Porosity, density and plug images are provided as accompanying information. The rock material originates from the Moffat Shale Group sampled from two shallow boreholes in Monaghan County, Ireland. Among the plug samples, 9 oriented pairs are used to derive anisotropy information of the frequency-dependent, complex electrical conductivity. The data have been processed by means of a Debye decomposition approach. The anisotropy is then determined by utilizing the foliation dip angle assuming tilted transverse isotropic conditions.