If your'e willing to loosen your definition of "clone" just a little bit, the same technique can be used in either direction.
As noted in another answer, duplicating the X chromosome from a male, while deleting the Y, has potentially serious problems, in that the result will resemble inbreeding in terms of genetic duplication for any genes carried on the X. Further, there isn't a practical way to create a Y from an X to go the other way.
So just adopt part of Mother Nature's method -- bring in donor chromosomes from an unrelated male (in the case of the male clone from female original) or female (vice versa). All other genes will be identical to the "parent's" genome, and by controlling which X is active (as noted in another answer, only single X is active in a female), the female clone from a male "parent" can be as identical as possible, while the male clone from the female "parent" will also be as identical as a male can be.
There is another option (not necessarily a good one) for cloning a female from a male "parent" -- just delete the Y and leave things alone. This will give a female child with Turner's Syndrome, most of the effects of which can be countered with hormone supplements at appropriate development stages. Probably unethical, but possible...