Far-infrared (IR) and submillimeter (15 [mu]m-1 mm) spectroscopy provides a powerful tool to probe a wide range of environments in the universe. In the past thirty years, many space-based observatories have opened the far-IR window to the universe, providing unique insights into several astrophysical processes related to the evolution of the early universe. Nonetheless, the size and cost of the cryogenic spectrometers required to carry out such measurements have been a limiting factor in our ability to fully explore this rich spectral region and answer questions regarding the very first moments of the universe. Among the key technologies required to enable this science are ultra-low-noise, far-IR, direct-detection spectrometers. In this thesis, Micro-Spec ([mu]-Spec) is proposed as a novel technology concept to enable a large range of flight missions that would otherwise be challenging due to the large size of current instruments and the required spectral resolution and sensitivity. [mu]-Spec is a direct-detection spectrometer operating in the 450-1000-[mu]m regime, which employs superconducting microstrip transmission lines to achieve a resolution (R >/= 1200) and be integrated on a ~10-cm2 silicon chip. The objective of this thesis is to explore the feasibility of the [mu]-Spec technology. First, analytical models are developed for the dielectric function of silicon compounds to be used as substrates in the transmission lines. These materials represent the ultimate source of loss in the system. The models are used to analyze laboratory spectral data of silicon nitride and oxide films and provide information on the loss within a 4% accuracy. A design methodology is then developed for the spectrometer diffractive region given specific requirements on size and spectral range. This methodology is used to explore the design space and find the optimal solutions that maximize the instrument efficiency and minimize the phase error on the focal plane. Five designs are described with different requirements and performance. Finally, analysis and calibration techniques are developed to study the properties of the superconducting materials employed in the transmission lines and detectors. These techniques are applied to laboratory data of molybdenum nitride and niobium to extract their quality factors and kinetic inductance fraction within a 1% accuracy.