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The Near-field Scanning Microwave Microscopy (NFSMM or simply SMM) employs the near-field interaction between a probe (source) and a sample to image and characterize materials with atomic resolution. In these systems, the probe excites the sample with microwave frequencies and generates a near-field focused in an extremely small area of the material surface. The microscope measures the local properties of the sample by collecting the response signal originated from this interaction, and the probe dimension mainly determines the resolution, rather than the excitation wavelength. Moreover, the SMM senses not only surface structures, but also electromagnetic properties up to a few micrometres below the sample surface, due to the microwave penetration. Despite the intriguing features and possible applications of the technique, the SMM presents some limitations summarized below: - limited bandwidth and sensitivity; - high number of parasitic components; - hypersensitivity to sample topography; As a consequence, many electromagnetic properties of the sample (beyond the sample topography) can be mostly invisible in SMM data, because the topographic contribution dominates and masks these effects. - incompatibility with the lossy liquid environment, such as inside saline solutions. This makes the application of SMM in bio-compatible environments highly challenging because live biological material is generally stored inside physiological solutions to survive. As a consequence, SMM is mainly limited to studies of semiconductor materials or inorganic surfaces, and it presents many difficulties for the analysis of non-flat and soft samples such as a living biological cell. In this context, the present manuscript illustrates some innovative technical solutions, in particular - a new technique for the real-time removal of unwanted topographic effects in SMM images. This method enabled us to reveal electromagnetic features of the material, that were hidden in the original data due to the hypersensitivity to sample topography; - a new microscope configuration called inverted Scanning Microwave Microscope. This setup has higher bandwidth and reduced parasitic components with respect to existing conventional SMM systems, it enables the local quantitative characterization of sample properties, and it is compatible with the physiological environment used to preserve live biological material. With this in mind, the present dissertation reports the main experimental results of the developed instruments and methodologies, illustrates their theoretical aspects, and discusses the range of applications of the proposed techniques, including the future directions of the research.

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