Bring water to boil in a large pot fitted with a rack. Carefully, put 2 empty half-pint (8 fluid ounces) Mason jars and their lids and screw-on bands in the water and boil for 10 minutes to sterilize them. Remove the jars, lids, and bands with tongs and set on paper towels to drain.

In a medium heavy-duty saucepan, crush the berries with a potato masher. Add 1/4 cup water (if using strawberries, add 1/2 cup water). Bring to a boil over medium-high heat, reduce the heat to medium low, and simmer until the berries are very soft and juicy, about 5 minutes.

Set a fine sieve over a bowl. Pour the berry pulp into the sieve and allow the juice to drip through. Gently press the pulp with a rubber spatula to extract as much juice as possible, but don't press so hard that you force the pulp through.

Clean the saucepan. Measure the juice and then pour it into the saucepan. For every 1/4 cup juice, add 1/4 cup sugar. Bring to a boil over medium heat, stirring to dissolve the sugar. Reduce the heat to low and simmer until the syrup is viscous but still runny, about 1 minute. Skim the foam with a spoon and pour the syrup into the sterilized jars. If you're not canning the syrup, put the jars on a wire rack and let cool to room temperature. Screw the lids and bands on and refrigerate the syrup for up to 2 weeks. If the syrup thickens during storage, stir to loosen it before serving. Serve warm or at room temperature.

Bring water to a boil in a large pot fitted with a rack insert. Carefully put 4 empty half-cup (4 fluid ounces) Mason jars (use 8 if you're doubling the recipe) or 2 empty half-pint (8 fluid ounces) Mason jars (use 4 if you're doubling the recipe) and their metal screw-on bands in the water and reduce the heat to a simmer; simmer until ready to use. Heat the lids in very hot water for 5 minutes to soften the flange. (Don't boil the lids when canning, as it might damage them and compromise the seal later.)

Remove the jars and rims with tongs, emptying the water from the jars. Pour the syrup into the jars, leaving about 1/4 inch of headroom. Wipe the rims clean of any spilled syrup and affix the metal lids onto the jars with the screw bands. Turn the bands only fingertip tight; don't close them as tight as you can, or you may compromise the seal.

Put the jars in the pot fitted with the rack insert and add enough water to cover by 2 inches. Bring to a boil over high heat, and boil briskly for 10 minutes.

Transfer the jars to a rack. Allow them to cool for 12 to 24 hours. You should hear a popping sound as the vacuum seals the lid to the jar. When the syrup is completely cool, check the seals by pressing on the lids. The lids should be taut and pulled down toward the inside of the jar. If a lid bounces when you press on it, the seal is imperfect, and you will have to repeat the canning process with a new lid, or simply refrigerate the syrup and use within two weeks. You can also remove the bands and try to pick up the jars by holding onto the rim of the lids. If the lids are tight, your seal is good.

Keep the bands in place when transporting the jars, but you do not need to store them with the bands on. Store in a cool, dark place for up to a year. Once a jar is opened, refrigerate the syrup for up to 2 weeks.

Make Ahead: Syrup that's not hot-water processed will keep in the refrigerator for up to two weeks.

Lemon Blueberry Syrup: Use blueberries and add 1/2 teaspoon finely grated lemon zest to the syrup while still hot.

Raspberry Mint Syrup: Use raspberries and crush three sprigs fresh mint with the berries.

Blackberry Thyme Syrup: Use blackberries and crush three sprigs fresh thyme with the berries.

Strawberry Balsamic Syrup: Use strawberries. While they syrup's still hot, add 3/4 teaspoon balsamic vinegar per 1/2 cup of syrup.

Serving Suggestions: Berry syrups are terrific on pancakes and ice cream or stirred into plain yogurt, rice pudding, and oatmeal. Or try brushing them over baked ham or a pork roast to create a sweet, fruity glaze. And for a delicious homemade soda, add one part syrup to two parts chilled seltzer water.