Researchers asked 75 heterosexual male volunteers to look at composite images of caucasian and Japanese female faces in a laboratory. The subjects could manipulate these faces by pressing a button to make them more or less "masculine," and were asked to select the face they would prefer for a long-term or short-term relationship. In a second experiment, 393 male participants participated in an online test where they selected which composite faces they preferred for a short-term or long-term relationship.
In both cases, men preferred feminine faces for a short-term relationship. This was especially true for men who reported being in relationships at the time of the study.
Of course, it's important to note that since the "masculine" and "feminine" faces were formed by a composite, and don't represent the full range of facial structures out there.
"The interesting question that results is why men do not prefer very feminine looking women all of the time," Anthony Little, the head researcher of the most recent study, told the Huffington Post in an email. "We speculate that men have to weigh up positive behaviour vs. looks and that men must consider more than just looks in considering a long-term cooperative relationships. Generally, I think men are often considered as only interested in attractiveness, and our study is suggestive that while this may be more true for short-term relationships, for long-term relationships personality and behaviour are important."
The look of a face matters when it comes to attraction, but so do mannerisms, voice, personality, smell and a host of other intangibles. Since we can't really change our faces, we'd probably all be best served trying to find romantic partners who we enjoy and who enjoy us back -- regardless of how "feminine" or "masculine" we look.