The ballistic transport of picosecond digital signals along terminated microstrip lines is a key feature of single flux quantum (SFQ) logic. In this work, we have used fast photoconductors driven by a femtosecond laser to measure directly for the first time the propagation and termination of picosecond pulses along Nb microstrip lines. Electrical pulses as short as 0.8 ps full-width-at-half-maximum (FWHM) have been measured. After propagating distances of 200 mu m, 1 mm, and 6.5 mm, the pulses broadened to 1.0, 1.2, and 1.8 ps (FWHM), respectively. In the frequency domain, attenuation is found to be negligible up to the gap frequency of Nb (0.7 THz), beyond which attenuation increases rapidly. We have also measured the reflections of the picosecond pulses off different terminations: open circuit, short circuit, and various resistors. The effective suppression of reflections with matched resistive loads is demonstrated up to frequencies approaching 1 THz.