Fill one-third of a medium saucepan with water and bring to a simmer. In a heatproof bowl, toss the berries with the sugar, cover with plastic wrap, and place over the simmering water. Heat the berries until they release their juices, about 1 hour. Line a fine-meshed sieve with cheesecloth, place over a bowl, and pour in the berry mixture. Strain well (do not press the berries or the juice will turn cloudy). Measure 1½ cups juice, chill, and reserve for the pearls and gelée.