Today there is a great need for communication between people and even between things, using systems onboard e.g. aircraft, cars, ships and satellites. As a consequence, these communications needs require antennas mounted on or integrated in the surfaces of different vehicles or platforms, i.e. conformal antennas. In order to ensure proper operation of the communication systems it is important to be able to determine the characteristics of these antennas. This thesis is about the analysis and design of conformal antennas using high frequency asymptotic methods. Commonly used eigenfunction solutions or numerical methods such as FDTD, FEM or MoM are difficult to use for arbitrarily shaped electrically large surfaces. However, the high frequency approximation approach together with an accurate ray tracing procedure offers a convenient solution for these surfaces. The geodesics (ray paths) on the surfaces are key parameters in the analysis and they are discussed in detail. In the first part of the thesis singly and doubly curved perfectly electrical conducting (PEC) surfaces are studied, with respect to the mutual coupling among aperture type elements. A synthesis problem is also considered where the effect of the mutual coupling is taken into account. As expected, the mutual coupling must be included in the synthesis procedure to be able to realize the prescribed pattern, especially in the shaped main lobe. Furthermore, the polarization of the antenna elements is very important when considering antennas on generally shaped surfaces. For such antennas the polarization must most likely be controlled in some way for a proper function. For verification of the results two experimental antennas were built at Ericsson Microwave Systems AB, Mölndal, Sweden. The first antenna is a circular cylinder with an array of rectangular waveguide fed apertures and the second antenna is a doubly curved surface (paraboloid) with circular waveguide fed apertures. It is found that it is possible to obtain very accurate results with the asymptotic method when it is combined with the Method of Moments, i.e. a hybrid method is used. The agreement compared to measurements is good at levels as low as –80 dB in many cases. The second part of the thesis is about the development of a high frequency approximation for surface field calculations on a dielectric covered PEC circular cylinder. When using conformal antennas in practice they have to be covered with a radome for protection and with the method developed here this cover can be included in the analysis. The method is a combination of two different solutions, one valid in the non-paraxial region of the cylinder and the other is valid in the paraxial region. The method is verified against measurements and reference results obtained from a spectral domain moment method code. / QC 20100616