Combine water, sugar, and honey in a nonaluminum pan and bring to a boil; skim off froth. Meanwhile, peel thin rind from 3 oranges; cut into very fine julienne strips. Add to syrup; simmer, partly covered, for 15 minutes, until tender.
Pare all white pith from peeled oranges. Remove both peel and pith from remaining 4 oranges. Halve them lengthwise, then cut ac