For example an archaeological find of a burial may contain coins dating to 1588, 1595 and others less securely dated to 1590-1625. The terminus post quem would be the latest date established with certainty, the coin that may have only reached circulation in 1595. The burial can only be shown to be 1595 or later. A secure dating of another coin to a later date would shift the terminus post quem.
An archaeological example of a terminus ante quem would be deposits formed before or beneath a historically dateable event, such as a building foundation partly demolished to make way for the city wall known to be built in 650. It may have been demolished in 650, 649 or an unspecified time before - all that can be said from the evidence is that it happened before that event.
Either term is also found followed by Latin non not. An example is in the supposed language dating method known as linguistic palaeontology. This holds (very controversially) that if the ancestor language of a family can be shown to have had a term for an invention such as the plough, then this sets a terminus ante quem non, a time-depth before which that ancestor language could not have begun diverging into its descendant languages. This has been used to argue against the Anatolian hypothesis for Indo-European because the date it implies is too early in that it violates the terminus ante quem non.