Hydrogen recombination lines are one of the major diagnostics of H II region physical properties and kinematics. In the near future, the Expanded Very Large Array (EVLA) and the Atacama Large Millimeter Array (ALMA) will allow observers to study recombination lines in the radio and sub-mm regime in unprecedented detail. In this paper, we study the properties of recombination lines, in particular at ALMA wavelengths. We find that such lines will lie in almost every wideband ALMA setup and that the line emission will be equally detectable in all bands. Furthermore, we present our implementation of hydrogen recombination lines in the adaptive-mesh radiative transfer code RADMC-3D. We particularly emphasize the importance of non-LTE (local thermodynamical equilibrium) modeling since non-LTE effects can drastically affect the line shapes and produce asymmetric line profiles from radially symmetric H II regions. We demonstrate how these non-LTE effects can be used as a probe of systematic motions (infall & outflow) in the gas. We use RADMC-3D to produce synthetic observations of model H II regions and study the necessary conditions for observing such asymmetric line profiles with ALMA and EVLA.