Vermouth makes an acceptable substitute for white wine in recipes. Nonalcoholic substitutes are more difficult to come by. For soups and pan sauces, the best course of action is to use extra broth, adding wine vinegar (red or white, depending on the recipe) or lemon juice just before serving.
To replace 1/2 cup White Wine:
1/2 cup broth + 1 teaspoon wine vinegar
1/2 cup broth + 1 teaspoon lemon juice
To test Jack Monroe’s idea, we compared a pot roast braised in a full bottle of Cabernet Sauvignon with another pot roast braised in an equal amount of black tea. The batch made with tea turned out to be surprisingly good, with the tannins in the tea helping balance the richness of the beef. We made this substitute even better by brewing a super strong infusion to bring out even more tannins and then adding a little vinegar for brightness.
For Red Wine:
Steep 1 tea bag (regular or decaffeinated) per 4 ounces of boiling water until tea is completely cooled, then stir in 1 teaspoon distilled white vinegar per 4 ounces of tea.
You can find more helpful tips on alcohol-free cooking in our Cook's Illustrated articles "A Great Alcohol-Free Sub for Red Wine" and "Best Pantry Subs to Replace the Alcohol in Your Cooking".