I think handling it like they do in James Bond movies is the best thing. The romance leads to the beginning of the event and then fade to black...

I would definitely follow up within the story. Obviously, these two characters now have strong feelings for each other. They will now have emotional entanglements and all that. Jealousy, protective instincts, fear for the other character's safety, etc. There were two characters in one of my campaigns that were intimate (offscreen) and they roleplayed these issues as you might expect.

On Going Beyond Stereotype

One of the ways the authenticity of female characters in movies are judged is called the Bechdel test. Essentially, if a movie has only one female character, or if it has more than one but they only talk to each other about men, it fails the test.

This is a good lesson to keep in mind when trying to fairly portray women in a roleplaying game, too. Unless you're playing a costume drama where words like "chattel" belong, your character will not be defined merely or even primarily by her relations to men, and she has many ways to be a woman that don't have to do with flirting or being hit on.

When you're GMing you're going to be playing a lot of women. You can use this to your advantage in doing convincing portrayals of women because you're going to have a variety to play. With one female character it's hard to play convincingly without overplaying it and stumbling into stereotype, or underplaying it and having gender fade out of view. With many female roles to switch among you can show off the variety of half of humanity (or elvenity, whatever):

• Play some female NPCs no differently than men
• Play some as stereotypes
• Play some as detailed personalities that are enmeshed in the cultural role of women in your game
• Play some as detailed personalities that reject the cultural role of women in your game
• Play some as mixes of two or more of those.

As the GM, by showing that your female NPCs are not all just the same cutout stereotype, you'll make all of your female NPCs much more convincing in the eyes of your players. If one NPC is (e.g.) a stereotype, then the variety will make it obvious that it's the character being an unfortunate stereotype and not just the GM being unable to play a more authentic character.

On the Differences Culture Brings

Undeniably, most cultures treat women and men differently, and as a result those women and men conduct themselves and behave differently in order to operate effectively in their culture. You'll have to make a decision for each of your cultures as to how strong the cultural pressure is for men and women to act differently, and for each character (both male and female) you'll have to make a decision about how strongly they accept or reject the explicit and unspoken rules their culture pushes on them. Using a technique like Lynn's answer about cultural cheat-sheets can be useful to zoom in on the defining attitudes of the culture, and to keep them present in your mind during play.

There are all kinds of great character details you can get out of this, and not all of them are going to be just about the differences of the genders either. (For example, thinking about characters this way might lead you to wonder what happens when an upstanding person nevertheless is outspoken in their rejection of the official religion.)

If you decide that the cultural pressures are slight to non-existent, you're going to have a very different set of characters—male and female—than if you decide that culture has moderate pressures to differentiate the genders. A culture with strong pressures is going to result in a very different set of characters again. (And in each of those, you'll get yet another very different set of characters if you decide to invert the way men and women are differentiated compared to our own culture.)

Finally, (assuming one of the cultural choices where women and men are somewhat to significantly distinct) there is a good article on portraying women as distinctly-gendered without leaning on stereotype or their relationships with men, written from the perspective of an avid female roleplayer: Saving Throw for Half Cooties: Gaming and the Femininely Advantaged.

For making female characters the article has sections on common creation mistakes to avoid, how growing up female makes a difference, and how the relationship influences of women are distinct from those of men. (It also has another half of the article about women as players, which is very worth reading but tangential to this question.)

The article also makes one of the best points for caring about how you portray women when roleplaying:

Often it is not a serious problem if gamers don't quite understand their character's mindset or fudge the details on behavior. It is just a game, and rarely will a real Mafia hitman or elven wizard be watching and criticizing the level of realism.

But when playing a character (or NPC) of a different gender/ethnic background than yourself, the line between poetic license and offensive stereotyping thins, especially if someone of that gender/ethnicity (or someone who is dating one) is sitting right across the table.

We can't be perfect, of course, but genuine care to make a good effort is enough in most people's books that imperfections will be forgiven, and you'll end up with a convincing female character despite being male yourself.