I don't think there is a limit, as to how high the frequency can get. The EM waves of the highest energy (and frequency) are called "gamma rays".
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Gamma rays have the highest energy in the electromagnetic spectrum. They have the shortest wavelengths and highest frequencies, making them the most energetic form of electromagnetic radiation.
The highest frequency in the electromagnetic spectrum is found in gamma rays. These rays have the shortest wavelengths and the highest energy levels of all electromagnetic waves.
Radio waves have the highest wavelength in the electromagnetic spectrum.
The highest frequency part of the electromagnetic spectrum is gamma rays. Gamma rays have the shortest wavelengths and highest energy of all electromagnetic waves.
There is no such thing as the highest frequency. Since photons or electromagnetic travel at the speed of light its frequency correlates to the energy. The highest energy, and thus the highest frequency, is found in cosmic radiation, where a single photon may carry many millions of kiloelectronvolts.