Antwerp is renouned as the diamond capital of the world, and you'll find it in the Flanders province of Belgium. Flanders has a moderate historic climate, the months of May and August offer the most sunny days.
As with other travel destinations within Belgium, May through September is the best time to go to Antwerp. Late spring is recommended for its long, northern days and good weather. Summer is also a good time to visit Antwerp, as the residents are on holiday in July and August.
September and October are fine times to visit, as tourists have left and the weather is still warm enough to be comfortable.
Flanders weather is known to be rather changeable, so be prepared. Rain is frequent but wait a while and it'll probably change. You might think about bringing an umbrella and sweather (or planning to buy them in Antwerp the first day it rains).
The chart below shows the historic high and low temperatures in Antwerp, with the rainfall chart below that.
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Hotel Elzenveld (value)
ibis Antwerpen Centrum (value)