The main goal of this work is the design and analysis of passive components employing metamaterial structures and in particular the wire medium metamaterial. Although there has been a lot of research interest in the physics of such metamaterial structures, there are not many resources available describing the behaviour of classical components, such as waveguides and cavity resonators, that are formed by metamaterials. Therefore, the aforementioned widely used devices, are realized with the deployment of the "Fakirs bed of nails" and their performance is analyzed. Our motivation is to expand existing analytical models and their applications to commonly used passive electromagnetic components, with a view to explore potentially new applications. As a means of study analytical techniques together with numerical simulations and measurements were used. This thesis is structured in the following chapters. The first chapter is an introduction to the basic principles of electromagnetics and their use on the framework of metamaterials; as illustrations some state of the art applications are presented. The next chapter is a literature review covering the work that has been done in the area of our main research interest (i.e., the Fakir's bed of nails as a metamaterial). An overview of the mathematics describing its behaviour is given as well as applications of the proposed structure. Attention has been paid on the latest studies because they provide complete physical insight. Some results from this chapter are used later as background knowledge for the analysis of passive components. This chapter is intended to lay the foundations for the reader to continue reading the rest of this work without the need to look in the literature. Chapter three investigates the dispersion effects in parallel-plate waveguides with both plates being realized by the Fakir's bed of nails. This chapter serves as an example as to how the Fakir's bed of nails can be used to form components. An analytical solution describing the behaviour of the waveguide is presented and compared against full wave numerical simulations. Chapter four presents a theoretical study of the resonant behaviour of metallic nanorods. A clear analogy between the coupled rods and the split rings/split squares is shown. The decline in the resonant frequency as the gap decreases, previously described in terms of self-capacitance, is interpreted by surface plasmons coupled across the gap. Chapter five presents a new enabling technology for implementing tunable rectangular waveguide components and circuits with the use of 2D and 3D metamaterials; a holey metal surface and wire media, respectively. As proof of concepts, results for tunable rectangular waveguide filters are presented with the use of pin block inductive irises and capacitive posts. Furthermore, by adapting the traditional metal-pipe rectangular waveguide for tunability, regions of the solid metal walls are replaced by holey metasurfaces. Prototype tunable structures were measured for verification and good agreement is achieved between full-wave numerical simulations and measurements. Chapter six analyzes a radically new design of waveguide verification device, suitable for measuring instruments such as Vector Network Analyzers. The device is designed to enable its roperties to be changed, by known amounts, after the device has been connected to the system that requires verification. The performance of the device is based on introducing relative changes in the transmitted and reflected signals and so is insensitive to errors introduced by waveguide flange imperfections. This makes the technique, in principle, ideally suited for waveguide VNAs operating at millimeter- and submillimeter-wave frequencies where these flange errors can dominate the measurements. A verification device is designed, simulated and tested in WR-15 waveguide (50-75 GHz). The last part of this thesis presents a rigorous analysis of lossy spherical cavity resonators starting from first principles. The electromagnetic field inside the spherical cavity is expanded in normal waveguide modes and the eigenfrequencies of the cavity resonator are obtained analytically by enforcing the appropriate boundary conditions at the cavity wall. Unlike perturbation techniques, used when low losses are present, there are no inherent limitations in the presented analysis and, therefore, its applicability range is much broader. Exact analytical results, acting as a benchmark reference standard, are compared to those generated independently by two commercial full-wave simulation software packages (HFSS and COMSOL). When the wall transforms from being a perfect electrical conductor to free space, as its intrinsic conductivity decreases from infinity to zero, it is found that the eigenmode solvers with both software packages increasingly fail. With both software packages, all possible modeling strategies have been investigated and their associated limitations identified. Moreover, a plane-wave approximation model is proposed that accurately predicts the numerical simulation results.