  It was shown by Faltings and Hriljac that the N\'eron-Tate height of a point
on the Jacobian of a curve can be expressed as the self-intersection of a
corresponding divisor on a regular model of the curve. We make this explicit
and use it to give an algorithm for computing N\'eron-Tate heights on Jacobians
of hyperelliptic curves. To demonstrate the practicality of our algorithm, we
illustrate it by computing N\'eron-Tate heights on Jacobians of hyperelliptic
curves of genus from 1 to 9.
