Non-alcoholic substitutes for wine are generally found in three categories – stocks, juices, and water. A veal, chicken, beef, or vegetable stock can add good flavor to savory dishes. Grape, apple, apricot, cranberry, or other juices (often watered down) can generally work well in sweet-ish dishes. Water doesn’t add flavor, but it adds the right amount of liquid and it also doesn’t impart unexpected flavor to very subtle dishes that might be “weirded out” by the addition of beef stock or cranberry juice.
Port is a sweet fortified wine, so you’d want to lean toward the juice category. If the dish you’re making is not really a sweet dish however, you might like to add a mixture of juice and a light stock or water, to add the modest sweetness found in the port but not so much sugar that your own and your students’ teeth involuntarily clench.