  The static electromagnetic properties of the $W$ boson, $\Delta \kappa$ and
$\Delta Q$, are calculated in the T-parity and non T-parity littlest Higgs
model (LHM) including terms up to the order of $(v/f)^4$, with $v$ the standard
model (SM) vacuum expectation value and $f$ the scale of the global symmetry
breaking. There are contributions from the virtual effects of the new heavy
particles and also from the new corrections to the SM vertices, which depend on
the mixing parameter $c$ and decrease quickly as $f$ increases. Depending on
the value of $c$, the partial contributions to $\Delta \kappa$ and $\Delta Q$
can add constructively or destructively. The terms of the order of $(v/f)^4$
are subdominant but they can add constructively and can enhance the $W$ form
factors for $f < 1$ TeV. In general the size of the $W$ form factors is very
suppressed in the LHM without T-parity as the constraints on the scale $f$ from
electroweak precision measurements are very tight. The LHM with T-parity has no
such constraints and it allows for values of $W$ form factors similar to those
found in other weakly coupled SM extensions, though they are out of the
expected sensitivity of future measurements at the LHC. We also discuss the
possibility that there is some enhancement due to the interactions arising from
the strongly interacting ultraviolet completion of the LHM.
