Slice the tomatoes about 1 cm thick or thinner. The thicker the slices, the longer the bake time. Try to keep the slices the same thickness so that they will all be done within roughly the same amount of time.
Line two baking sheets with tin foil, shiny side up. Place a cooling rack on top. If you don't have cooling racks, you can place them right on the foil but then the cooking time will be even longer.
Preheat oven to 325 degrees Fahrenheit.
Arrange the slices of tomatoes in a single layer on the sheets with the cut side facing up. Stir together the olive oil and maple syrup and brush on the tomatoes with a pastry brush. Sprinkle with salt.
Bake for 2-3 hours. Rotate pans every hour or so. The tomatoes are done when they are mostly shrivelled up.
Store in the fridge as there is still a high enough water content for them to spoil at room temperature.
Eat as is or use in soups, stews, pasta sauces, etc.