So in my last session I introduced a new NPC, namely a beautiful heiress who turns out is the patron behind the party's jobs...After asking the player, sounds like he wants to pursue a relationship.
As a GM, I always find this flattering. If an NPC is interesting enough to a player that they want to become involved, then I consider it a great complaint on my ability to craft NPCs. So, kudos.
After reading up on some advice on romance, I've decided it's going to stay pg.
Yes, good idea. However, 'pg' or even 'g' by no means precludes serious romantic relationships. It just means that you 'draw a curtain' over some of the events that are private between those two characters. Probably the greatest example in all of literature of this is the wedding night scene between Marius and Cosette in Hugo's 'Les Miserables'. There is certainly plenty of romance implied in say 'Sleeping Beauty' or in 'The Sound of Music'. We don't need to follow Maria and Captain Von Trapp on their honeymoon, yet of course if you actually think about it, every sort of intimacy is implied by that without needing an 'R' rating.
Likewise, as the cinematographer/director, you as the GM have the right and power to frame scenes as you need to and cut scene such that you imply whatever you need to imply has happened without having it happen on stage. I would argue that for the health of the table, you often need to do exactly that. You can still engage adult story lines, you just don't have to be graphic about it. With care I think you can actually imply anything, which is often much more impactful than just showing it. Intellectual romance or horror is often more powerful than visceral forms. You are engaging a different part of the brain - more ape, less lizard.
But it still begs the question, should there be mechanics or just role play?
Well, I think that there should be _some_ mechanics but for interactions as deep as romance it should be mostly just role play because few systems are going to be nuanced enough to approach the subject of romance in a good way. This is not something that comes down to a single check nor is it something where any check/challenge should be inorganic. The only real need of mechanics here is deal with the characters charisma or lack of it appropriately. But you should be quite liberal in judging the situation.
Does it make sense for the personality of the NPC? What does the NPC want? Is there a logical match here? Does it make sense as a story? What are the NPCs morals like? How might the NPC approach this relationship?
The mechanics should only be informing the direction of the story, and not setting it. A high charisma PC might be magnetic, but may run into problems that his very magnetism is in the long run working against him if that isn't what the NPC wants from a relationship. The low charisma PC may have problems getting the NPC to take him seriously, regardless of the suitability of the match. Use mechanics to determine whether individual scenes flop or not.
Role playing I think gives a more organic feel, but the downside would be the awkwardness of the whole thing potentially.
No offense, but get over it. You're the GM. Your supposed to be leading the table in developing its skill and immersion based on you skill as a RPer. If you as a GM are embarrassed to RP, you are setting a poor example for the table. You made the responsible decision to keep things PG. You set an adult limit. After that, you don't have a lot excuses.* Let the player draw the line and learn how to frame so that the action can be said to occur with awkward details. "You kiss.", is perfectly fine narration of consequences. If you feel that the second person might be too awkward, back down to third person, "They kiss.", and move the scene to narration. The potential awkwardness is a problem, but deal with that as it is encountered. I have once been thrown for a loop by a 'romance' situation, so I can sympathize, but honestly that was my failing for being caught off guard - and I told my player so. I would normally see this sort of thing coming, as I'm usually pretty good about predicting how players will react to an NPC, but this was a potential crush by the player I hadn't considered.
Another method could be to use a relationship score and have acts add or take away. This I fear trivializes relationships by just rolling then up into a number.
What do you all think?
I think you are right about it trivializing things.
Let me say that in general, real life courtship is often a long and complex affair. There is no need to cut to the chase any time soon. If the character is pursuing an NPC relationship in a serious manner, treat it as a serious story line. The heiress is presumably a complex person with feelings and preexisting relationships that the PC may be entirely unacquainted with. Don't make her exist in a vacuum. There could be rival suitors, old flames, societal considerations, disapproving family members, etc. On top of that, there is the matter of time and place - is now really a good idea to be starting a romance? And in any society there are forms that have to be observed and acceptable norms of behavior. They certainly don't have to be modern norms. Consider the sorts of barriers to romance typical in a Jane Austin story (or a Tolkien story for that matter).
*All that being said, I don't think that you need to be as comfortable with everything as Abed in the Community episode, nor do I think the sort of graphic descriptions implied by the scene are actually healthy. It's best understood as parody (I hope), because otherwise I suspect this would be game wrecking in one of two ways. Either lots of people are going to be uncomfortable, or else you'll jump the shark and be running nightly erotica sessions - ruining the game in the same fashion that say Rand and Aviendha's encounter jumps the shark in 'Wheel of Time' and begins to pervert the focus of the writer away from the larger epic themes he'd introduced and towards the more tedious melodrama that ultimately prevents him finishing the story before he dies.