"Whom" is correct, and it is still permissible there in highly formal writing, I think. "Whom" is dying, and it is normally seen only immediately after a preposition. "Patients to whom you recommend various methods of contraception" is probably better, anyway, because the reader has to wait a long time for that "to" the other way.
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CashtanchikPatients whom you recommend various methods of contraception toWith to all the way at the end, whom looks rather silly there.