Using the data sets taken at center-of-mass energies above 4 GeV by the BESIII detector at the BEPCII storage ring, we search for the reaction e(+)e(-) -> gamma(ISR) X(3872) -> gamma(ISR)pi(+)pi(-) J/psi via the Initial State Radiation technique. The production of a resonance with quantum numbers J(PC) = 1(++) such as the X(3872) via single photon e(+)e(-) annihilation is forbidden, but is allowed by a next-to-leading order box diagram. We do not observe a significant signal of X(3872), and therefore give an upper limit for the electronic width times the branching fraction Gamma B-X(3872)(ee)(X(3872) -> pi(+)pi(-) J/psi) < 0.13 eVat the 90% confidence level. This measurement improves upon existing limits by a factor of 46. Using the same final state, we also measure the electronic width of the psi(3686) to be Gamma(psi)(ee)(3686) ee = 2213 +/- 18(stat) +/- 99(sys) eV. (C) 2015 The Authors. Published by Elsevier B.V.