By analogy with the coherent interaction of short (on the scale of relaxation times) light pulses with inverted, i.e., active, and non-inverted, i.e., passive, two-level quantum systems, we study the possibility of the nonstationary amplification, self-induced transparency, and compression effects for the microwave electromagnetic pulses propagating along quasi-stationary electron beams. The considered analogy is not of only general physical, but also practical significance since a number of practically interesting transformation modes of ultrashort pulses, including the microwave superradiance pulses, can be implemented on its basis. The first experiments, in which the nonstationary amplification during the pulse—electron-beam interaction in a waveguide with dielectric insert was observed and pulses with subgigawatt peak powers at a carrier wavelength of 8 mm and uniquely short durations less than 100 ps were obtained, are described.