This paper considers the suitability of a number of emerging and future instruments for the study of radio recombination lines (RRLs) at frequencies below 200 MHz. These lines are of interest because they arise only in low-density regions of the ionized interstellar medium and because they may represent a frequency-dependent foreground for next-generation experiments trying to detect H i signals from the Universe's Epoch of Reionization and Dark Ages (so-called "21-cm cosmology" observations). We summarize existing decametre-wavelength observations of RRLs, which have detected only carbon RRLs. We then show that, with reference to an interferometric array, the primary instrumental factor limiting detection and study of the RRLs is the areal filling factor of the array. We consider the first station of the Long Wavelength Array (LWA-1), the LOw Frequency ARray (LOFAR), the low-frequency component of the Square Kilometre Array (SKA-lo), and a future Lunar Radio Array (LRA), all of which are likely to operate at decametre wavelengths. Key advantages that many of these arrays offer include digital signal processing, which should produce more stable and better defined spectral bandpasses; larger frequency tuning ranges; and better angular resolution than that of the previous generation of instruments that have been used in the past for RRL observations. Detecting Galactic carbon RRLs, with optical depths at the level of 10 −3 , appears feasible for all of these arrays, with integration times ranging from a few hours to as much as 100 h; at optimal frequencies this would permit a Galactic survey. The SKA-lo and LRA, and the LWA-1 and LOFAR at the lowest frequencies, should have a high enough filling factor to detect lines with much lower optical depths, of order 10 −4 in a few hundred hours. The amount of RRL-hosting gas present in the Galaxy at the high Galactic latitudes likely to be targeted in Epoch of Reionization and Dark Ages H i studies is currently unknown. If present, however, the spectral fluctuations from RRLs could be comparable to or exceed the anticipated HI signals.