  Common extensions of the Standard Model of particle physics predict the
existence of a "hidden" sector that comprises particles with a vanishing or
very weak coupling to particles of the Standard Model (visible sector). For
very light (m < 10^-14 eV) hidden U(1) gauge bosons (hidden photons),
broad-band radio spectra of compact radio sources could be modified due to weak
kinetic mixing with radio photons. Here, search methods are developed and their
sensitivity discussed, with specific emphasis on the effect of the coherence
length of the signal, instrumental bandwidth, and spectral resolution. We
conclude that radio observations in the frequency range of 0.03--1400 GHz probe
kinetic mixing of ~10^-3 of hidden photons with masses down to ~10^-17 eV.
Prospects for improving the sensitivity with future radio astronomical
facilities as well as by stacking data from multiple objects are discussed.
