Garden tomatoes retain their quality for only a short time once ripe. Slowing down the ripening process allows you to stretch a crop of fresh tomatoes so you can use them over a three- to four-week period. You can't stop ripening completely without ruining the flavor of the tomatoes, but proper storage does allow you to slow the process down substantially. You can quickly ripen any remaining green tomatoes once you are ready to use them.
Wrap each tomato individually in brown paper or a sheet of newspaper. The paper prevents the buildup of ethylene gas produced by ripening tomatoes, which speeds up ripening, from affecting the rest of the tomatoes.
Place the wrapped tomatoes in a box, stacking them no more than two to three layers deep. Store the box in a 55-degree Fahrenheit location. Warmer temperatures speed up ripening while lower temperatures cause the fruit to develop less flavor.
Check the tomatoes weekly and remove any that have ripened fully. Regularly removing the ripe tomatoes prevents the ethylene gas from affecting the remaining stored tomatoes, allowing the rest of the tomatoes to ripen slower.