  We present results for the electromagnetic form factors of the proton and
neutron computed on the $(2 + 1)$-flavor Coordinated Lattice Simulations (CLS)
ensembles including both quark-connected and -disconnected contributions. The
$Q^2$-, pion-mass, lattice-spacing, and finite-volume dependence of our form
factor data is fitted simultaneously to the expressions resulting from
covariant chiral perturbation theory including vector mesons amended by models
for lattice artefacts. From these fits, we determine the electric and magnetic
radii and the magnetic moments of the proton and neutron, as well as the Zemach
radius of the proton. To assess the influence of systematic effects, we average
over various cuts in the pion mass and the momentum transfer, as well as over
different models for the lattice-spacing and finite-volume dependence, using
weights derived from the Akaike Information Criterion (AIC). Our results for
the magnetic moments of the proton and neutron are in good agreement with the
experimental values and have a relative precision of about $2.4\,\%$ and
$3.7\,\%$, respectively. For the electromagnetic radii of the proton, we
achieve a precision at the $1.5\,\%$ level.
