First, clean the aubergines and fish (remove the ends from the aubergines and skin and central bone from the fish) and cut them into cubes, possibly of similar size.
Fry the aubergines with oil and a little salt in a large non-stick pan for at least 10 minutes, then set them aside.
In the same pan, brown the onion and celery, then add the fish and brown it for a couple of minutes, stirring often.
Add the washed and chopped cherry tomatoes, salt and cook for about ten minutes, stirring occasionally.
When the cherry tomatoes have softened, add also aubergines and pitted olives.
Once the cooking surface has dried, add the sugar, then raise the heat and blend with the vinegar, stirring constantly until everything has evaporated, then turn off the heat and add the chopped basil.
The swordfish caponata is ready: serve it warm or cold.