Classical heraldry starts around 1100 when shield designs became tied to noble lineages. But the practice of decorating your shield to make it recognisable is much older. Roman military units used distinctive shield markings. And Ancient Greek hoplites are depicted (both in contemporary and historic pictures) as having symbols painted on their shields.
Now, I know that Sparta used letter Lambda Λ (other name for Sparta was Lakedaimōn), and that Athenians used the little owl on their coins and generally as a symbol of their city. But, does anyone know of any other cities having their distinct symbols? Except for Spartans, there doesn't seem to be unity in what symbols hoplites had on their shields; were those inherited in a heraldic manner, from father to son, or were they completely arbitrary? I can't find a lot of useful info, maybe I just don't know what to look for.