A theory is presented for propagation of electromagnetic waves concentrated in the vacuum-gap sheath region separating a plane conductor from a cold magnetoplasma. The applied static magnetic field is parallel to the conductor and in the direction of wave propagation. The theory predicts propagation at all frequencies between zero and the upper-hybrid frequency divided by √2. Experimental results are reported in which resonances caused by the wave reflection at the end of a thin cylindrical antenna aligned with the magnetic field are used to determine the sheath-wave dispersion relation. The effect of the antenna bias, plasma density and antenna diameter on the dispersion relation are studied experimentally and the results are compared with the plane-surface theory. In spite of the difference between the theoretical and experimental geometries, qualitative agreement is noted with respect to variations in magnetic field, plasma density, sheath thickness and antenna radius. The prediction that the presence of an applied magnetic field raises the upper sheath wave cutoff frequency has been confirmed experimentally, as well as the prediction that the presence of the sheath allows propagation above the cyclotron frequency. In particular, both theory and experiment show the existence near the cyclotron frequency of a special frequency at which the sheath-wave wave number is independent of the plasma density.