Hyperbolic metamaterial (HMM) based resonators have emerged as a very promising tool for providing highly enhanced as well as directional emission from a quantum emitter. HMM provides high- k hyperbolic modes to the radiation emitted from a quantum emitter embedded inside the HMM. These high-momentum hyperbolic HMM modes are coupled into free space by an antenna, which overcomes the large mismatch between free-space modes and HMM modes. Recently, cylindrical metallic antennas were observed to be the most effective in overcoming this momentum mismatch. In this work, we try to understand how this free-space out-coupling of emission from a quantum emitter embedded inside the HMM, with a cylindrical plasmonic antenna over the HMM’s top surface, varies as a function of frequency (or wavelength). HMM mode hyperbolicity was observed to increase with an increase in the emission wavelength, leading to its effective coupling to a cylindrical antenna. However, for large excitation wavelengths, the absorption cross section of the plasmonic cylindrical antenna was found to be significant. This leads to increased radiation losses within the plasmonic antenna, leading to a reduction in the collection and quantum efficiency of the coupled system. The performance of the HMM coupled cylindrical plasmonic antenna was observed to have a Gaussian envelope type profile, having peak performance in the range of 1000–1100 nm, with maximum collection and quantum efficiencies reaching 52% and 70%, respectively.