Place the blueberries and lime zest in a covered saucepan with 1 tablespoon water and cook gently, shaking the pan occasionally, until very soft (about 10 minutes.). Press through a fine sieve into a heatproof bowl or the top of a double boiler, then stir in the butter and sugar and put over a saucepan of gently simmering water; do not allow the bottom of the bowl to sit in the water. Heat gently, stirring, until the sugar has dissolved and the butter has melted.
Strain in the eggs and continue to stir over gently simmering water until the curd thickens enough to coat the back of the spoon, which should take 30-40 minutes. Stir only occasionally at first, more frequently as the cooking progresses, then constantly toward the end so that the curd cooks evenly and does not curdle. The water must not boil.
Strain the curd, if necessary, into clean, dry jars. Refrigerate up to 2 weeks.