Sponsor an Orphan
In some ways, sponsoring (supporting) an orphan seems to be the ultimate form of child sponsorship: after all, looking after orphans is something which both the Bible and the Koran give priority to, and equally Humanist common sense dictates that a child who does not have a parent to care for them has the greatest need. It is also easier in some ways since there are no issues of a child sponsorship undermining the status of the child's natural parents, although the time commitment for caring for a child with no biological parents may well be longer (until the child is independent).
There are challenges though: when you find a child alone it is not always possible to know if they are orphaned or not. After natural disasters, SOS Children is often given responsibility for all unaccompanied children whilst destruction is at its worst. We care for the children whilst we determine which children have surviving relatives able to look after them. Typically out of many thousands of children needing immediate help, only dozens turn out to be actually orphaned and in need of a new family.
In the run up to World Orphan Week, SOS Children ran an editorial about the number of orphans in the world, pointing out that some NGOs exaggerated the actual number of orphans to try to tug on Western heart strings. That this can have unintended consequences, such as people arriving to take the "orphans" home with them (think of the American missionaries after the Haiti earthquake), is a lesson some are slow to learn.
Anyway, if you feel that child sponsorship is best for looking after orphaned and abandoned children, SOS Children or a similar orphan charity is where to go next.