Wash, halve, and pit the apricots. Optionally, treat with lemon juice to prevent browning.
Combine the sugar and water (or juice) in a saucepan (see notes for quantities). Bring to a boil, stirring until the sugar is dissolved.
Place jars in boiling water for 10 minutes to sterilize. Keep the lids simmering in a separate pot of hot water.
Pack apricot halves into hot, sterilized jars. Pour warm syrup over the fruit, leaving 1/2 inch of headspace.
Wipe jar rims, add lids and bands, and tighten the bands until fingertip tight.
Process in a water bath canner. Times for raw pack are for 25 minutes for pints and 30 minutes for quarts. For hot pack, times are 20 minutes for pints and 35 minutes for quarts. For pressure canning, process for 10 minutes at 6 lbs pressure. Be sure to adjust for altitude, see notes below.
Let jars cool completely, check seals, and store. Properly canned and sealed jars can be stored on the pantry shelf indefinitely without spoiling, but quality starts to deteriorate after 12-18 months. Refrigerate after opening.