Home Postcodes by state WA 6010 Postcode 6010 6010 is the postcode for 5 localities in WA: Claremont, Claremont North, Karrakatta, Mount Claremont and Swanbourne. Localities with postcode 6010ClaremontWAClaremont NorthWAKarrakattaWAMount ClaremontWASwanbourneWA Postcode 6010 State or territory Western Australia (WA) Localities 5 Council area Claremont; Nedlands; Mainly Claremont, partly Nedlands Council area based on Australian Bureau of Statistics data (ASGS Edition 3), CC BY 4.0. Postcode 6009 · Postcode 6011