How to Grow Tomatoes in Aquaponics. Aquaponic systems grow fish in a water tank and use crops such as tomatoes to filter the tank water before it returns to the fish. The crop gets its nutrients from the tank water. Due to the somewhat experimental status of aquaponics, as of 2010, and the initial expense and the wide variety of set-ups being used both for research and for commercial production, you should have aquaponic systems professionally installed. Once set up, growing tomatoes in an aquaponic system is simple and highly productive.