Microwave techniques have been widely used to characterize properties of conventional superconducting systems. Examples include characterizing the magnetic penetration depth of bulk crystals and thin films, residual resistance of superconducting radio-frequency cavity systems for use in particle accelerators, and resonance properties of superconducting microwave electronic circuit components such as coplanar waveguides and Josephson junction devices.

In recent decades, new types of superconducting systems have appeared and massive characterization efforts have been made through low frequency techniques such as transport resistivity measurement, quantum oscillations in electrical resistance and magnetic susceptibility, scanning tunneling microscopy, optical frequency techniques, X-ray, angle-resolved photoemission spectroscopy, and Raman spectroscopy. On the other hand, microwave characterization of these new systems has been less frequent. As the diversity of an ecosystem helps the system to be more robust, the diversity of scientific measurements provides a more thorough understanding of a physical system because of the complimentary advantages of each measurement. The advantages of the microwave technique are first, it is non-destructive since the measurement does not require galvanic contact between the probe and the sample. Second, it has a good signal-to-noise ratio because it employs sensitive high frequency instruments and techniques. Third, the microwaves only marginally perturb the system under investigation since the photon energy of the probing signal is typically much lower than the maximum superconducting energy gap, which is not the case for optical techniques.

In this thesis, unconventional superconducting systems, such as superconductors with non-s-wave pairing symmetry and superconductors with non-trivial topology, are investigated by means of microwave techniques. The thesis consists of two parts. In Part 1, I will discuss a newly developed microwave superconducting gap spectroscopy system. Using a combination of resonant microwave transmission technique and laser scanning microscopy, I demonstrated that the new technique can directly image the pairing symmetry of superconductors with unconventional pairing symmetries. During the demonstration with an example d-wave superconductor, a signature of Andreev bound states was also found. A phenomenological model to explain the observed properties of the Andreev bound states is also discussed. Lastly, an effort to broaden the adaptability of the new technique to samples of more general morphology is discussed.

In Part 2, I describe a microwave surface impedance technique and its application to the characterization of topological superconducting systems. A thickness dependent surface reactance study of an artificial topological superconductor SmB6/YB6 (topological insulator / superconductor bilayer) was used to determine the characteristic lengths of the system (normal coherence length, penetration depth, and thickness of the topological surface state), and revealed robust bulk insulating properties of SmB6 thin films. A surface resistance and reactance study on the candidate intrinsic topological superconductor UTe2 revealed the existence of residual normal fluid and a chiral spin-triplet pairing state, which together point out the possible existence of an itinerant Majorana normal fluid on the surface of chiral superconductors.