Radio-frequency fields in the GHz range are increasingly applied in biotechnology and medicine. In order to fully exploit both their potential and their risks detailed information about the dielectric properties of biological material is needed. For this purpose a measuring system is presented that allows the acquisition of complex dielectric spectra over 4 frequency decade up to 110 GHz. Routines for calibration and for data evaluation according to physicochemical interaction models have been developed. The frequency dependent permittivity and dielectric loss of some proteins and nucleic acids, the main classes of biomolecules, and of their sub-units have been determined. Dielectric spectra are presented for the amino acid alanine, the proteins lysozyme and haemoglobin, the nucleotides AMP and ATP, and for the plasmid pET-21, which has been produced by bacterial culture. Characterisation of a variety of biomolecules is envisaged, as is the application to studies on protein structure and function.