You can use a router on quartz countertops, but there are a few things you need to keep in mind. First, because quartz is harder than most countertop materials, you'll need to use a carbide-tipped bit designed for hard materials. Second, you'll need to be very careful not to damage the surface of the quartz with the router. In general, it's best to practice on a scrap piece of quartz before attempting to rout your countertop.