This thesis introduces, for the first time, Stepped Impedance Resonator (SIR) bandpass filters (BPF) based on Composite Right/Left-Handed (CRLH) transmission lines. In other words, a novel approach in design of BPFs for RF and microwave applications is successfully proposed and examined, which can serve both miniaturisation and performance enhancement purposes. In conducting this research, design, development and optimisation procedures and techniques for the proposed BPFs have been presented. Theoretical, numerical and experimental results have confirmed that these filters are capable of significantly reducing the size while maintaining the integrity of the filter performance; and in some cases, extensively enhancing the performance.Two Gammag/4-type CRLH SIRs are designed and characterised based on the available equations. ADS lumped-element equivalent circuit model and HFSS full-wave electromagnetic simulation, and measurement results prove that both CRLH SIRs surpassed their RH counterparts, in terms of both size and performance. Indeed, comparison of the first CRLH SIR with its RH counterpart revealed a 35% size (length) reduction. The second CRLH SIR design is measured to be 66% smaller than its RH counterpart and 14% smaller than the initial CRLH SIR. In addition, simulation and measurement results reveal that an intelligently designed CRLH SIR shows a better quality factor Q and input impedance |Zin| response, and provides higher design flexibility. Phase unwrapping and energy (current) flow analysis have been used to prove left-handedness of the CRLH SIRs.The concept is extended to propose multi-section (Gammag/2-type and tri-section SIRs) and tunable CRLH SIRs. Numerical analysis and obtained results show that the Gammag/2-type CRLH SIR benefits from a 45% size (length) reduction compared to its RH counterpart, and a better |Zin| response. The results obtained from the tri-section CRLH SIR (TSSIR), clearly show that the TSSIR is capable of relocating (and minimising) the multiple spurious resonance frequencies, while maintaining the same fundamental frequency f0. As such, no spurious frequency is observed before 8 GHz. Also, measurements indicated that the CRLH TSSIR is not only 30% smaller in length compared to its RH counterpart, it was even 28% smaller than a two-section RH SIR resonating at the same frequency of 2.5 GHz. In addition, the tuning capability of the ferrite CRLH SIR is illustrated when the operating frequency of the resonator is tuned from 5.1 GHz to 5.4 GHz, and 5.65 GHz for H0 = 2000, 2250, and 2500 Oe, respectively.These SIRs are then combined and configured to form two main categories of CRLH SIR bandpass filters: PCB filters based on RT Duroid and MMIC filters based on GaAs. In both filters, the homogeneity condition has been satisfied by ensuring that the longest length is much less than Gammag (in this case l = Gammag/12) for PCB-based filters and l = Gammag/14 for MMIC filters at the centre frequency of the filters. The first PCB-based CRLH SIR filter, which has been designed to operate at 2.75 GHz, is measured 24mm × 28mm. HFSS 3-D full-wave simulations and measurement results of this filter reveal that, with an insertion loss of -2.6dB and return loss of -21.5dB, the filter not only has a very good selectivity, but also is extremely efficient in extending the free-spurious stop-band, pushing the first spurious response to around 11 GHz (about 4×f0). The second PCB-based CRLH SIR filter has much smaller size, measuring overall filter dimensions of 6mm × 5.14mm. This filter also benefits from a smaller resonator size, improved overall coupling and a more controllable circuit. Theory, full-wave simulation and measurement results demonstrate that, with an insertion loss of -1dB and return loss of -34dB, the miniaturised CRLH SIR filter proves very successful as it was about 80% smaller in size compared to its RH counterpart with the same centre frequency, while maintaining the integrity of the filter performance. Moreover, the miniaturised CRLH SIR BPF is significantly more controllable in its dimensions and response due to the fact that more elementary parameters are available in the CRLH configuration.The MMIC CRLH SIR bandpass filters are then proposed with an emphasis on further size reduction with maintenance (or enhancement) of their transmission responses. As such, two classes of MMIC filters were designed: the first one is very small measuring 3.2mm × 3.4mm, with an insertion loss of -5.3dB at the centre frequency 3.1 GHz. The filter also shows good attenuation both before and after the passband with its first spurious frequency occurring at 13.52 GHz (i.e. > 4×f0). The second set of MMIC filters employed multilayer topology to reduce the filter size. It has been clearly shown that with an intelligent design, the size (dimension) limitations of the PCB-based filters have been overcome by using the MMIC technology, resulting in filters with significantly reduced sizes - design I: 1.32mm×3.35mm, and design II: 1.4mm × 1.5mm. It has also been observed that MMIC structures are generally exposed to inevitable losses, though steps can be taken to reduce such losses.