We discuss the generation and propagation of nondiffracting twisted pulses at microwaves, obtained through polychromatic spectral superposition of higher-order Bessel beams. The inherent vectorial structure of Maxwell's equations has been considered to generalize the nondiffracting solution of the scalar wave equation with azimuthal phase variation. Since a wide frequency bandwidth is necessary to synthesize time-limited pulses, the non-negligible wavenumber frequency dispersion, which commonly affects the propagation in the microwave range, has been taken into account. For this purpose, a higher-order Bessel beam is generated by enforcing an inward cylindrical traveling-wave distribution over a finite aperture. We present and discuss the main aspects of the generation of twisted pulses in the microwave range, showing the promising possibility to carry orbital angular momentum through highly focused …