Slot dipole antennas fed by coplanar waveguide (CPW) on substrates consisting of a single dielectric layer exhibit various attractive qualities, including significantly wider impedance bandwidth than comparable microstrip patch antennas. For applications that call for unidirectional radiation, such as antennas on airframes, a conducting back plane is needed. A CPW on a conductor-backed single-dielectric-layer substrate will always experience power leakage into the TEM parallel-plate mode. On the other hand, it is possible to design CPW lines on conductor-backed two-layer substrates that are free from leakage into the substrate. However, once the CPW is used as feed line to a slot dipole, power leakage into the TM0 substrate mode caused by the transition between the CPW and the radiating slot, and by the radiating slot itself, may still severely compromise radiation efficiency. This study has two main contributions to offer. First, a paucity of work on CPW-fed slot antennas on conductor-backed two-layer substrates is alleviated by providing a fuller characterization of single-slot behaviour on two-layer parallel-plate substrates than is currently available, and by systematically investigating a practically feasible minimum antenna configuration, namely broadside twin slots, that is not debilitated by the problem of substrate mode leakage. Results obtained with the moment-method-based electromagnetic simulator IE3D that emphasize the trade-off between radiation efficiency and impedance bandwidth are presented: they can be used for design purposes. For instance, with respect to single slots on a substrate with an electrically thin top dielectric layer and an air bottom layer, it is shown that radiation efficiency increases and bandwidth decreases as height of the bottom substrate layer increases. For broadside twin slots, it is demonstrated that spacing close to half a wavelength of the two-layer parallel-plate TM0 mode apart can yield a large improvement in radiation efficiency over that of a single slot (a reduction in bandwidth however occurs). The second main contribution is the development of an approach for finding the mutual admittance Y12 between CPW-fed slots on conductor-backed two-layer substrates that can be more readily incorporated in an iterative array design procedure than a moment-method-based technique, yet is of comparable accuracy: it is built on a standard reciprocity-based expression. As an initial step, the mutual admittance between CPW-fed slots on a conductor-backed two-layer substrate with an air bottom layer is characterized using IE3D. This involves presenting curves for Y12 between twin slots against slot separation d along standard paths for slot half-lengths in the vicinities of the first and second resonant half-lengths of the corresponding isolated slots (such data might be used towards a first-order array design), and a study of the effect of back plane distance (i.e., bottom layer height) on mutual coupling. The bulk of the thesis however is devoted to the above reciprocity-expression approach. Simplifying assumptions are outlined that make it possible to determine Y12 against d by performing a once-only moment-method analysis of each slot in isolation, and then calculating external and internal reaction integrals at each value of d. This is significantly more economical than carrying out a full moment-method analysis of the whole twin-slot structure at every instance of d. Evaluation of the internal reaction integral requires the appropriate component of the spatial-domain Green's function for the substrate, which is derived in a form containing Sommerfeld-type integrals: treatment of singularities is discussed. The reciprocity-expression approach is verified by comparing Y12 against d curves for twin slots and non-identical slot pairs on a variety of conductor-backed two-layer substrates to IE3D simulations. A procedure that involves judicious selection of reference planes is introduced by which agreement between the methods for the special case of twin slots with the same half-length as the corresponding isolated second-resonant slot can be even further improved. A measurement is provided that validate theoretical calculations.