Ports are highly controlled environments and do not allow visitors. They have multiple layers of security and other restricted zones.
In short - unless you work for a logistics company, you can't get inside the port.
This is true not just in Antwerp, but pretty much anywhere there is a port that handles international cargo.
It would be like asking to visit the area of the airport where they process all the luggage and get it ready for loading on airplanes.
The best you can hope is a tour of the waterways; for example on the Flandria:
You can choose an extensive port cruise or the ‘Best of Antwerp’
cruise, in which you improve your knowledge of the port and the city
as you slip past on the Scheldt.
In the mood for something more? Then go for one of the theme cruises.
Savour the atmosphere on an Aperitif Cruise, for example, or enjoy
Antwerp at sunset during the Candlelight Cruise. Or why not go on a
scrumptious tour of discovery with the Beer, Chocolate & Diamonds
You can get a breath of fresh air on the outside deck or hunker down
in the cosy atmosphere of the indoor lounge, as you enjoy the
tranquillity of the water and the beautiful view of the Antwerp
skyline and the banks of the Scheldt. Welcome aboard!