Yes, absolutely. The Romans, for example, got most of their salt from brine refineries, salinae. Minus the modern equipment for moving loads around, they worked much as some modern ones do: large flat open ponds that progressively dry the water out of the brine, leaving salt residue behind.

Here's a textual description in Pliny, Natural history 31.81-83 (starting at the point marked 'Artificial salt' in the margin); he also describes refineries that dry the brine using wood-fires, something that would be rather extravagant nowadays.

There were major brine refineries in Cyprus, Tarentum in south Italy (a lagoon), Tuz Gölü (a salt lake) in Turkey, Chott el Jerid in Tunisia, and of course at Rome's own harbour, Ostia. Here's an aerial view of Tarentum from Google Earth that may help give an idea of why it was such a suitable location for salt extraction. But there were smaller refineries all over the place: H. E. M. Cool's 2006 book Eating and drinking in Roman Britain reports (p. 56)

(Salt) was produced by evaporation. Many salterns were to be found in areas such as the Fenland, and the coasts of Essex, Kent and the southern counties. The manufacturing process involved trapping seawater, which has a salt content of about 3%, in shallow ponds and tanks. ... When the salt level had risen sufficiently so that it formed a supersaturated solution (at least 26%), the salt could be made to precipitate by heating the brine. ... Salt could also be produced away from the coast at the brine springs of Cheshire and Worcestershire. These produced brine that was already supersaturated, so no preliminary evaporation was needed.

In the warmer Mediterranean climate the precipitation by heating wasn't always necessary -- though the military writer Vegetius does devote some attention to how to produce salt by precipitation in a besieged city. There was plenty of salt that came from mines and salt pans too.

There's a good history of ancient salt production waiting to be written: Kurlansky's 2002 book on the history of salt is reliable as far as it goes, but he isn't an expert on the ancient material.

Anyway, whatever its source, salt was produced on an enormous scale, because of its importance both to human health, as a preservative, and as a fertiliser. As a result it was reasonably cheap (contrary to popular myth). Cool reports that at Vindolanda in Britain, salt cost about 1/15 the price of bacon, weight for weight. In another post I've provided the figures to show that in Rome around 200 BCE, 330 g of salt cost about 1/32 of a regular soldier's daily wage.