Both in terms of physical dimensions, and in terms of how much trade would go through the port in a given day how large was the port?
The present day ruins will give you a pretty good idea of the size. There were separate port areas for commercial and military shipping. Google maps link below:
Carthage had two connected ports. The inner war harbor was circular with an island in the middle. It was said to be able to hold 300-350 warships, mostly biremes and triremes. The outer harbor was larger and could hold many merchant ships. Both could be blocked by great chains across the entrances.
http://www.ancientmilitary.com/carthage-trade.htm
Both ports are still visible today. The two ports together are about 3,200 feet long and 1,000 feet wide.
Here are some images, modern and reconstructions, of what the port might have looked like in Carthaginian times: