What is the ruling on wooing a widow with the intention of marrying her?

Flirting with a non-mahram woman is absolutely forbidden, whether she is a widow or otherwise, and regardless of the purpose of the flirting. It is permissible to hint at proposing to a non-mahram woman while she is in her 'iddah (waiting period), and to explicitly propose after her 'iddah has ended. Among the permissible hints are for a man to say: "Someone like you is desirable," or "You are indeed virtuous," or "You know that I am of good lineage or wealthy," and similar statements from which the desire for marriage can be understood.