There is a robust upper limit on the energy of synchrotron radiation in high-energy astrophysics: ∼mec2/α, where α= 1/137 is the fine structure constant and the value refers to the comoving frame of the fluid. This is the maximal energy of synchrotron photons which can be emitted by an electron having an arbitrarily high initial energy after it turns by angle ∼π in the magnetic field. This upper limit can be naturally reached if the converter mechanism contributes to the jet radiation and can be imprinted in spectra of some blazars as a cut-off or a dip in the GeV range. We use numerical simulations to probe the range of parameters of a radiating jet where the ultimate synchrotron cut-off appears. We reproduce the variety of spectra depending on the source luminosity and on the scale of the emission site. We also compare our results with the EGRET blazar spectra in order to illustrate that the agreement is possible but still not statistically significant. The predicted feature, if it exists, should be observed by Fermi in spectra of some blazars.