Paulo, the Coast Guard, though having lots of peacetime missions, is also a military service, and they and their predecessor services (the Revenue Cutters of the Treasury Dept) took in all major wars at sea.
So the Captain of the Port is typically a Coast Guard Captain, or Commander. And they have much authority to order ships to move,or not move, depending on the security needs of the port or any other event which requires such action in the interest of safety, preservation of the port, and the like. So sounds not unlike your Navy Port Captains.
A blurb on Coast Guard history from the 'good book' Wikipedia ;-)
And the need to go to the Admiral is to make sure this rather drastic step of ordering someone not to sail from a nice harbor on a nice day because of what might happen later at sea, isn't overused of taken in haste by some Lieutenant down on the waterfront. Usually Admiral follows the recommendation of the Captain of the Port, who knows his/her Lieutenants.