Vapor-cell atomic clocks based on double resonance are high-precision instruments that have strong potential for industrial commercialization. They offer performance which is superior to quartz oscillators and are already employed for synchronization-demanding applications in telecommunication and smart power grid networks. With a volume of up to few liters, these are devices compact enough to qualify for space applications related to global positioning. Moreover, a new generation of high-performance vapor-cell clocks based on Pulsed Optical Pumping scheme (POP) showed performance approaching that of much larger frequency standards. For the case of the pulsed clock, the magnetic field homogeneity plays a central role in limiting the performance -- in order to fully exploit the advantages of the novel POP scheme it is critical to apply a constant (amplitude) field distribution across the atomic sample. The main objective of the thesis is to find and characterize a cavity solution that is appropriate to apply in compact high-performance vapor-cell atomic clocks, and more particularly in the case of the pulsed optically pumped scheme. In the currently existing solutions a relatively large type of cavity is utilized for which in order to obtain field homogeneity a small fraction of the field is sampled. A major drawback of this approach is the negatively affected compactness. Moreover, such a cavity is more restrictive to the useful volume of the atomic sample, and it is more complicated to stabilize in terms of temperature. We propose a solution for which we managed to obtain a nearly constant microwave magnetic field distribution along the direction of the optical field with more than 97% of orientation uniformity across the atomic sample. Our approach is to implement a cavity with artificial magnetic conductor boundary conditions in order to take advantage of a beneficial field mode with two zero variation indexes.