Polarized radio synchrotron emission from interstellar, intracluster and intergalactic magnetic fields is affected by frequency-dependent Faraday depolarization. The maximum polarized intensity depends on the physical properties of the depolarizing medium. New-generation radio telescopes such as Low Frequency Array (LOFAR), the Square Kilometre Array (SKA) and its precursors need a wide range of frequencies to cover the full range of objects. The optimum frequency of maximum polarized intensity (PI) is computed for the cases of depolarization in magneto-ionic media by regular magnetic fields (differential Faraday rotation) or by turbulent magnetic fields (internal or external Faraday dispersion), assuming that the Faraday spectrum of the medium is dominated by one component or that the medium is turbulent. Polarized emission from bright galaxy discs, spiral arms and cores of galaxy clusters are best observed at wavelengths below a few centimetres (at frequencies beyond about 10 GHz), haloes of galaxies and clusters around decimetre wavelengths (at frequencies below about 2 GHz). Intergalactic filaments need observations at metre wavelengths (frequencies below 300 MHz). Sources with extremely large intrinsic rotation measure | RM | or RM dispersion can be searched with mm-wave telescopes. Measurement of the PI spectrum allows us to derive the average Faraday | RM | or the Faraday dispersion within the source, as demonstrated for the case of the spiral galaxy NGC 6946. Periodic fluctuations in PI at low frequencies are a signature of differential Faraday rotation. Internal and external Faraday dispersion can be distinguished by the different slopes of the PI spectrum at low frequencies. A wide band around the optimum frequency is important to distinguish between varieties of depolarization effects.