This thesis explores a new range of electromagnetic structures made available by a subtle change in the interpretation of how resonators interact. The focus is on microwave filters and antennas that are essential to wireless communication. The standard interpretation is that filters and antennas are made from a series of intercoupled resonators, with multiple paths through the structure allowing transmission zeros that increase selectivity and isolation between ports. This thesis instead begins with the assumption that the resonators of multi-mode structures are more effectively interpreted as not interconnected at all, being perfectly orthogonal to each other. The resonators are now equivalent to the structure’s eigenmodes and couple only to the ports, in parallel, with the phase and amplitude relationships of these parallel external couplings allowing a generalised frequency response with maximum transmission zero flexibility. This thesis aims to improve the size, cost and performance of filters and antennas using parallel-coupled multi-mode resonating structures by contributing six novel implementations.The first contribution introduces a bandpass filter made from a parallel coupled, triple-mode, silver-plated, surface-mounted ceramic cube, with a novel coupling topology featuring over-coupled single-mode input/output quarter wave stripline resonators. A single cube achieves class leading ratio of quality factor to volume (Q/V), three flexibly placed transmission zeros and allows a simple cubic construction without the need for chamfers for inter-resonator coupling. To validate the proposed design and analysis method, multiple filters are designed and simulated. Moreover, two DCS-1800 Band-3 (utilized in mobile communications) single cube transmit filters are fabricated and measured.The second contribution is a duplexing filter with high isolation. The device is based on triple mode filters that are built using silver plated ceramic cubes. To create a six-pole, six-transmission zero filter in the DCS-1800 band, two cubes are cascaded. To improve spurious harmonics, low dielectric caps are placed on the cube faces. These caps push the first cube spurious up in frequency by around 340 MHz compared to the uncapped cuboid, allowing a 700 MHz spurious free window. To verify the design, a DCS-1800 duplexer with 75 MHz wide bands is built. It achieves around 1 dB of insertion loss for both the receive (Rx) and transmit (Tx) ports with around 70 dB of mutual isolation within only 20 MHz band separation, using a volume of only 30 cm3. It is estimated that a similarly specified coaxial cavity duplexer would need a volume of at least 300 cm3.The third contribution is a triple-mode silver-plated ceramic cavity bandpass filter with wide spurious-free response. It uses single mode ceramic slabs as interfacing resonators with the triple-mode cube to give wide spurious-free performance up to 4 GHz for an 1800 MHz base-station filter. Three square apertures at the slab-cube interface give simple and flexible control of transmission zero placement while maintaining low insertion loss. The parallel nature of the slab-to-cube coupling allows a simple cubic structure without chamfers or inter-mode coupling elements. A seven-pole filter in the DCS-1800 transmit band using a slab-slab-cube-slab-slab structure is built and measured. The filter achieves 1 dB of band edge insertion loss with more than 50 dB of attenuation, 20 MHz from the band edges, from an 11 cm3 package. The wideband response shows more than 40 dB of attenuation up to the frequency 3.7 GHz.The fourth contribution is a triple-mode band-stop ceramic cavity filter utilizing parallel-coupled resonators. A transmission line, etched onto the face of a silver-plated ceramic cube, couples to three modes in parallel, avoiding any inter-resonator coupling perturbations. By varying only a few structural parameters, the coupling strengths into each mode can be controlled, and highly flexible band-stop filtering functions are demonstrated. A 30 MHz band-stop filter at 1800 MHz, from a roughly 27 mm3 ceramic block mounted to a copper base, is fabricated and measured. It achieves 26 dB of attenuation, with less than 0.3 dB of insertion loss 20 MHz away from the stop-band, and less than 0.3 dB of reflection loss in the stop-band, closely matching the simulation.The fifth contribution demonstrates a generalised frequency response for cavity filters from six modes coupled in parallel. The six modes belong to two parallel-coupled triple-mode spheres and are coupled in parallel via two half-wavelength transmission line resonators. The theory of phase and amplitude control of parallel couplings into spherical cavities is introduced by way of coupled resonator models, and the structure of two combined spheres is detailed. The theory and simulations prove that multiple transmission zeros can be arbitrarily placed, including inside the passband to create multiple bands and beyond infinity (imaginary frequencies) for flattened group delay. Several design examples of two spheres in parallel are presented to demonstrate a high degree of flexibility of transmission zero placement, and one example is fabricated and successfully tested.The sixth contribution reinterprets the assumption that mutual coupling is the mechanism that leads to the degradation of isolation between the active ports of antenna arrays. It is shown that a coupled-resonator model with series-coupled mutual coupling breaks down when applied to multi-mode/multi-port antenna arrays and limits the achievable isolation. An improved model based on parallel-coupled modes is presented. This model suggests that poor isolation is more accurately caused by unbalanced antenna modes. Using this model, several novel examples of simple and compact dual- and triple-mode antennas show how to maximize isolation in multi-mode antennas by balancing the modes’ resonant frequencies and radiation bandwidths. For comparison, the mutually coupled assumption limits isolation to around 20 dB in the proposed novel structures whereas 40 to 70 dB is possible when parallel-coupled modes are considered. Based on the developed concept, a compact triple-mode two-pole-filtering antenna is fabricated at 3500 MHz with 160 MHz of bandwidth and more than 40 dB of isolation between the antenna ports.