Gauged vortices are configurations of fields for certain gauge theories on fibre bundles over a surface $S$. Their moduli spaces support natural $L^2$-metrics, which are Kaehler, and whose geodesic flow approximates vortex dynamics at low speed. My talk will focus on vortices in line bundles, for which the moduli spaces are modelled on the spaces of effective divisors on $S$ with a fixed degree $k$; I shall describe the behaviour of the underlying $L^2$-metrics in a "dissolving limit" where the $L^2$-geometry simplifies and can be related to the geometry of the Jacobian variety of the surface. Some intuition about multivortex dynamics in this limit will be provided by analysing the simplest nontrivial example (two dissolving vortices moving on a hyperelliptic curve of genus three). This is joint work with N. Manton.