The knowledge of mechanisms underlying interactions between biological systems, be they biomacromolecules or living cells, is crucial for understanding physiology, as well as for possible prevention, diagnostics and therapy of pathological states. Apart from known chemical and direct contact electrical signaling pathways, electromagnetic phenomena were proposed by some authors to mediate non-chemical interactions on both intracellular and intercellular levels. Here, we discuss perspectives in the research of nanoscale electromagnetic interactions between biosystems on radiofrequency and microwave wavelengths. Based on our analysis, the main perspectives are in (i) the micro and nanoscale characterization of both passive and active radiofrequency properties of biomacromolecules and cells, (ii) experimental determination of viscous damping of biomacromolecule structural vibrations and (iii) detailed analysis of energetic circumstances of electromagnetic interactions between oscillating polar biomacromolecules. Current cutting-edge nanotechnology and computational techniques start to enable such studies so we can expect new interesting insights into electromagnetic aspects of molecular biophysics of cell signaling.