The highest measured frequencies of EM waves are Gamma-rays and are typically produced from the decay of atomic nuclei.  The most powerful sources of gamma-rays (and usually the sources with the shortest wavelength) are caused by astronomical events.  Recently there was a very strong gamma-ray burst from Cygnus-A, the super-massive black hole at the center of the Milky Way Galaxy.  It is estimated that the gamma ray burst was the result of the black hole gobbling up something with three times the mass of the Earth.

There is no theoretical upper limit for the frequency of gamma-rays.  To make one bigger than what we've seen so far will require starting with a super-massive black hole and something much larger than the Earth.  Not quite reproducible in the laboratory.