I think there are tests they do to determine if conception has occurred.  If it has not, they will give the woman contraception.  But perhaps they could still give contraception even if a pregnancy has occurred--provided that it is a true contraceptive drug and not an abortion inducing drug.  Then it would not matter if conception had occurred.  

What is or is not most "effective" is not the point.  The point is that it is never morally justifiable to murder an innocent human being.  To suggest an abortion is  a more effective treatment in this case is like saying killing the poor is more effective at combating poverty!

As for tubal ligation--the women can have her child and go to a secular hospital and get her tubes tied if she wants.  By the way--pregnancy can still occur when the tubes are tied.