Any starship owned by the Crystals may perform the Lay Web Mines mission as long as it has fuel and torpedoes.
Web mines are small devices filling a circle around a point in space. Any enemy starship passing through a web minefield has a fairly high chance of hitting a web mine. A web mine hit will stop any starship and drain some of its fuel, doing a small amount of damage in the process. Any vessel which spends any great length of time within a web field will be drained large amounts of fuel each turn, rendering it potentially vulnerable to tow capture.
Details of the process and effects are described in the minefields page.
See also: Out of Fuel.