It is difficult and expensive to match the sensitivity of the most sensitive vertebrate ears with off-the-shelf microphones due to the self-noise of the sensor. The extremely small apertures of microelectromechanical microphones create options to use horn waveguides to amplify sound prior to transduction without resulting in an unacceptably narrow directivity. Substantial gain can be achieved at wavelengths larger than the horn. An analytical model of an exponential horn embedded in a rigid spherical housing was formulated to describe the gain relative to a free-field receiver as a function of frequency and angle of arrival. For waves incident on-axis, the analytical model provided an accurate estimate of gain at high frequencies as validated by experimental measurement. Numerical models, using the equivalent source method, can account for higher order modes and comprehensively describe the acoustic scattering within and around the horn for waves arriving from any direction. Results show the directivity of horn receivers were adequately described by the analytical model up to a critical wavelength, and the mechanisms of deviation in gain at high frequencies and large angles of arrival were identified.