A systematic procedure is described to predict the noise emissions from realistic aero-propulsive jets. Large Eddy Simulation (LES) is used to compute the jet flowfield and coupled with the Ffowcs Williams and Hawkings (FW-H) equation for far-field noise predictions. A low-dissipation fifth-order upwind biased finite-volume reconstruction procedure is used along with selective fourth order inviscid flux blending. Higher order explicit time integrators are used for enhanced wave propagation. Also, non-contiguous block interfacing is employed to eliminate the traditional limitations of structured grid topologies for complex geometries. For simple jet configurations the LES/FW-H method is validated with University of Mississippi's National Center for Physical Acoustics (NCPA) experimental measurements. Four unique and more realistic applications are then shown. The first is a hot faceted jet with lobed corrugations, followed by an over-expanded military gas turbine engine exhaust with and without chevrons. Then a twin jet impinging on a jet blast deflector is shown, and lastly are two high aspect-ratio nozzles, one with and one without a bevel. The LES/FW-H methodology is shown to produce reasonable agreement with experimental measurements at modest grid resolutions. Details are discussed about the selected example problems highlighting the challenges associated with applying the tools to realistic geometries and jet configurations.