A hybrid method which combines the uniform geometrical theory of diffraction (UTD) with a numerical moment method (MM) technique is presented for the analysis of the radiation from a composite slot-blade cavity-backed antenna located on realistic aircraft configurations. The excitation of the antenna is due to a delta gap generator in a thin-wire probe feed that is placed inside a rectangular cavity. The MM procedure is used to solve coupled integral equations that are formulated for the unknown equivalent electric current distribution on the blade and the unknown equivalent magnetic current distribution over the slot, when this slot-blade antenna configuration resides on an infinite ground plane. The UTD is next used to efficiently and accurately calculate the radiation from these equivalent current distributions for the slot-blade antenna combination when the latter are now located on realistic aircraft geometries instead of a fiat ground plane. Calculated radiation patterns of the composite slot-blade cavity-backed antennas placed on a Boeing 737 commercial airplane and an F-16 fighter aircraft are presented to illustrate the utility of this hybrid approach.