Preheat oven to warm, below 200°. Remove seeds from tomato halves but not the fibrous tissue. Place tomatoes, cut side up, on baking sheet lined with aluminum foil. Sprinkle with salt, pepper and marjoram; place in oven and leave 12 hours. You want to dry, not cook, the tomatoes; if they are drying out too quickly, prop open oven door a little. The tomatoes will darken and wrinkle. Small tomatoes may take only 12 hours, but large ones may need up to 24 hours.
Pack tomatoes in warm, sterilized jars and cover with olive oil. Seal, allow to cool; store in refrigerator for up to a month. Makes 1 pint.
Add a lighter flavor to sauces and pasta salads than commercial sun-dried tomatoes.