We report measurement of the cross section of e(+)e(-) -> pi(+)pi(-)psi(2S) between 4.0 and 5.5 GeV, based on an analysis of initial state radiation events in a 980 fb(-1) data sample recorded with the Belle detector. The properties of the Y(4360) and Y(4660) states are determined. Fitting the mass spectrum of pi(+)pi(-)psi(2S) with two coherent Breit-Wigner functions, we find two solutions with identical mass and width but different couplings to electron-positron pairs: M-Y(4360) = (4347 +/- 6 +/- 3) MeV/c(2), Gamma(Y(4360)) = (103 +/- 9 +/- 5) MeV, M-Y(4660) = (4652 +/- 10 +/- 8) MeV/c(2), Gamma(Y(4660)) = (68 +/- 11 +/- 1) MeV; and B[Y(4360) -> pi(+)pi(-)psi(2S)] . Gamma(e+e-)(Y(4360)) = (10.9 +/- 0.6 +/- 0.7) eV and B[Y(4660) -> pi(+)pi(-)psi(2S)] . Gamma(e+e-)(Y(4660)) = (8.1 +/- 1.1 +/- 0.5) eV for one solution; or B[Y(4360) -> pi(+)pi(-)psi(2S)] . Gamma(e+e-)(Y(4360)) = (9.2 +/- 0.6 +/- 0.6) eV and B[Y(4660) -> pi(+)pi(-)psi(2S)] . Gamma(e+e-)(Y(4660)) = (2.0 +/- 0.3 +/- 0.2) eV for the other. Here, the first errors are statistical and the second systematic. Evidence for a charged charmoniumlike structure at 4.05 GeV/c(2) is observed in the pi(+/-)psi(2S) intermediate state in the Y(4360) decays.