  Given a compact Riemann surface $\Sigma$ of genus $g_\Sigma\, \geq\, 2$, and
an effective divisor $D\, =\, \sum_i n_i x_i$ on $\Sigma$ with
$\text{degree}(D)\, <\, 2(g_\Sigma -1)$, there is a unique cone metric on
$\Sigma$ of constant negative curvature $-4$ such that the cone angle at each
$x_i$ is $2\pi n_i$ (see McOwen and Troyanov [McO,Tr]). We describe the Higgs
bundle corresponding to this uniformization associated to the above conical
metric. We also give a family of Higgs bundles on $\Sigma$ parametrized by a
nonempty open subset of $H^0(\Sigma,\,K_\Sigma^{\otimes 2}\otimes{\mathcal
O}_\Sigma(-2D))$ that correspond to conical metrics of the above type on moving
Riemann surfaces. These are inspired by Hitchin's results in [Hi1], for the
case $D\,=\, 0$.
