My mother made us "grilled" cheese sandwiches using Velveeta, Italian bread and pressed it between sheets of foil using a hot iron. The same iron used for clothes. They were sublime - Velveeta and all. Since my wife started hiding the iron when I used this method, I had to find an alternative.
Today, I made a light lunch of small sandwiches with various meats and cheese. I lightly oiled a cast iron skillet (on bottom) and placed another cast iron pan on top. In this case, I used a dutch oven because it was pretty heavy. While a true panini press would have a heated top element, I can simply turn the sandwiches and cook them one side at a time. The top weight is nice because it insures the sandwiches make good contact with the bottom skillet and get nice and crisp. The whole sandwich melds together physically as flavorfully (I know it's not a word). They were very nice. A nice variation on this would be to use a ribbed cast iron pan to give the nice looking grill marks; they're cheap too.