  We calculate the electromagnetic form factors of the nucleon up to fourth
order in manifestly Lorentz-invariant chiral perturbation theory with vector
mesons as explicit degrees of freedom. A systematic power counting for the
renormalized diagrams is implemented using both the extended on-mass-shell
renormalization scheme and the reformulated version of infrared regularization.
We analyze the electric and magnetic Sachs form factors, $G_E$ and $G_M$, and
compare our results with the existing data. The inclusion of vector mesons
results in a considerably improved description of the form factors. We observe
that the most dominant contributions come from tree-level diagrams, while loop
corrections with internal vector meson lines are small.
