  The nucleon-pion-state contribution to QCD two-point and three-point
functions relevant for lattice calculations of the nucleon electromagnetic form
factors are studied in chiral perturbation theory. To leading order the results
depend on a few experimentally known low-energy constants only, and the
nucleon-pion-state contribution to the form factors can be estimated. The
nucleon-pion-state contribution to the electric form factor $G_{\rm E}(Q^2)$ is
at the +5 percent level for a source-sink separation of 2 fm, and it increases
with increasing momentum transfer $Q^2$. For the magnetic form factor the
nucleon-pion-state contribution leads to an underestimation of $G_{\rm M}(Q^2)$
by about 5 percent that decreases with increasing $Q^2$. For smaller
source-sink separations that are accessible in present-day lattice simulations
the impact is larger, although the ChPT results may not be applicable for such
small time separations. Still, a comparison with lattice data at $t\approx 1.6$
fm works reasonably well.
