One of the outstanding problems of terahertz (THz) spectroscopy is the measurement of the underlying vibrational spectrum of a molecular solid, where individual vibrational transitions are often merged into broad absorption features by line broadening processes. In this talk I describe how this problem can be addressed using the technique of waveguide terahertz time-domain spectroscopy (THz-TDS). In this technique an analyte molecular film is deposited on one of the inner surfaces of a single-mode metal parallel plate waveguide (PPWG) with a 50 micron gap between the plates. The vibrational spectrum of the film is then measured in a sensitive manner using sub-picosecond THz pulses confined within the PPWG over a relatively long pathlength of a few centimeters. I will show how waveguide THz-TDS (applied at cryogenic temperatures) has proven useful in resolving the underlying vibrational fingerprint spectrum of a variety of explosives solids in the frequency range between 0.2 THz – 4.0 THz, with linewidths of individual transitions as narrow as 7 GHz (0.21 cm 1), and line frequencies determined to a precision of 1 GHz (0.03 cm-1). I’ll also discuss how these highly resolved spectra are currently being modeled using solid state computational methods.