Guitar strings have harmonics because they are tied at both ends, leading to a countable (one for every positive integer) set of sinusoidal solutions. Because the highest-frequency vibrations attenuate the most quickly, no matter how you push or pull on the guitar string to get it started it will quickly end up in a vibration state that can be described almost entirely in terms of the first few normal modes.
When radio waves are tied at both ends (like in an antenna that is not infinitely long), you can find similar resonance phenomena. This is why the size of the antenna is often chosen based on the intended wavelength of reception. If a broad-band pulse were emitted near a radio antenna that wasn't driving any load, the resistance in the wire would quickly filter out the higher modes, leaving an analogue of the guitar string situation. However broadband pulses are avoided as much as possible and disconnected antennas are rare, so this situation is not often considered.