For an eggcrate structure, you can use strips of styrene, and cut halfway through the horizontal members, then halfway through the verticals from the other side. When finished and glued, prime and airbrush with Alclad chrome or polished aluminum
One quick and dirty method that doesn't look super, but works in some cases, is to get a silver gel roller pen. Cut a piece of styrene to fit the opening, and rule in the lines with the silver pen over the flat black styrene. Then glue in place.