This PhD research focuses on designing wearable and flexible high radio-frequency (RF) structures with soft conductors and flexible substrates. These structures are designed to operate from 20 to 40 GHz, including antennae, and high-impedance surfaces (HISs). This frequency range is chosen because it covers the unlicensed industrial, scientific and medical (ISM) band (24 GHz), and two candidate licensed frequency bands (28 and 38 GHz) for future 5th Generation (5G) wireless networks. This research firstly proposed a new hybrid transmission-line method for accurate and quick characterisation of flexible dielectric materials, in which two error boxes are introduced so that the effects of impedance mismatch due to transmission line discontinuity at the interfaces can be largely removed. Next, a fabric-based coplanar waveguide (CPW) antenna is designed and a flexible fractal electromagnetic bandgap (EBG) structure is proposed to enhance its performances such as bandwidth and radiation gain. A series measurements and experiments are conducted for the EBG-backed CPW antenna, including free-space, bending and on-body measurements. The final part of this research project first presents some preliminary analysis and experiments on temperature sensing antennas along with a few discussions on the measured results. This is followed by a study on the dielectric response of selected common fabrics to ambient humidity at millimetre-wave frequencies. Based on the characterised results, a humidity sensing antenna operating at 38 GHz is designed and fabricated. The result shows that the resonant frequency of the designed antenna has a relatively linear response to ambient humidity and a high sensing resolution of 26 MHz per 1% relative humidity (RH).