Context. Attenuation of the TeV γ-ray flux from distant blazars through pair production with extragalactic background light leads to the development of electromagnetic cascades and subsequent, lower energy, GeV secondary γ-ray emission. Due to the deflection of VHE cascade electrons by extragalactic magnetic fields (EGMF), the spectral shape of this arriving cascade γ-ray emission is dependent on the strength of the EGMF. Thus, the spectral shape of the GeV–TeV emission from blazars has the potential to probe the EGMF strength along the line of sight to the object. Constraints on the EGMF previously derived from the gamma-ray data suffer from an uncertainty related to the non-simultaneity of GeV and TeV band observations. Aims. We investigate constraints on the EGMF derived from observations of blazars for which TeV observations simultaneous with those by Fermi telescope were reported. We study the dependence of the EGMF bound on the hidden assumptions it rests upon. Methods. We select blazar objects for which simultaneous Fermi/LAT GeV and Veritas, MAGIC or HESS TeV emission have been published. We model the development of electromagnetic cascades along the gamma-ray beams from these sources using Monte Carlo simulations, including the calculation of the temporal delay incurred by cascade photons, relative to the light propagation time of direct γ-rays from the source. Results. Constraints on the EGMF could be derived from the simultaneous GeV–TeV data on the blazars RGB J0710+591, 1ES 0229+200, and 1ES 1218+304. The measured source flux level in the GeV band is lower than the flux of the expected cascade component calculated under the assumption of zero EGMF. Assuming that the reason for the suppression of the cascade component is the extended nature of the cascade emission, we find that B ≳ 10-15 G (assuming an EGMF correlation length of  ≥1 Mpc) is consistent with the data. Alternatively, the assumption that the suppression of the cascade emission is caused by the time delay of the cascade photons the data are consistent with B ≳ 10-17 G for the same correlation length.