If you drink carefully matched wine with your dish, only still water is appropriate, a clear distinction between main character (wine) and supporting cast (water) is necessary.

But there is a slight difference between red and white wine: With white wine, choose water with a low mineral content and a neutral pH; red wine demands water with a medium to high mineral content and a neutral pH.

The water should have a slightly higher temperature than the wine to prevent taking attention away from the wine. Think about stemware too, most reputable producers of wineglass series offer water glasses that complement the wineglasses.