Now, this has probably been done before, but it just occured to me today:
- Excuse me... I've lost my car keys... Could I borrow your phone to call a friend for a lift?

Call your own phone with hers and let it ring... make sure it's switched off)

- No answer but thanks anyway ; I'll get a cab

Walk away and send her a text 2 mins later:
Getting your number was sooo easy Now, no tricks, how about a coffee?

Lame and extremely weird no offense. Put yourself in the girls shoes, you haven't gamed her at all and just played a sneaky trick on her. You're still a stranger. Hope this helps.

_________________
Learn how I picked up hundreds of girls online without leaving home! Click on the link for your free guide, 7 Secrets to Online Attraction!
http://attractionkings.com

No offense taken, and I haven't field-tested it...
Sneaky... yes... lame... idk, this is subjective... it'd make me laugh if someone did that to me... I think it might depend on the girl.

First I want to say that it's awesome that your thinking outside of the box, that will help you a lot as you progress.

Second I want to say don't do this one. This one has an extremely high probability of giving off the "I'm a stalker rapist" vibe. Generally speaking any "sneaky method" for getting into contact with a girl like this one, or hunting a girl down on facebook etc... is going to work against you for at least 2 reasons. First the creepy factor as mentioned above, but also it gives of the impression that you lack the confidence to man up and talk to her and try for her number upfront. Honestly I think this would work some small part of the time, however that part of the time would be when the girl basically already wants to do you based strictly off how you look.

Try something like this instead, it's not much longer and will yield much more solid numbers for you.

step 1: smile and wave when she looks at you, I also like to mouth "hi" while I do this and do it from some distance.

If she smiles your looking good on to step 2, if she doesn't move on.

step 2: walk up to her and say something. This is going to be personality dependent but I recommend something situational, a comment involving something around her, or in the close surroundings. I like to say go about this part in a silly/semi-sarcastic type of tone... keep it light keep it funny. Also using lines from movies (comedy not romance) is usually money.

If she smiles or laughs your doing good. Keep with it until you've been talking for 2-3 minutes... think about 2 paragraphs worth of talking if it was on paper.

step 3: There are a bunch of ways to go for closes, but until your more comfortable I'll just give 2 examples. The first one will get you more numbers but some of those will turn out not to be that into you, the second will get a few rejections up front but the numbers you get will almost always be girls who are interested.

1) Hey I'm having a party this weekend, you should come *hand her your phone*, put your number in there and I'll let you know when and where

2) I love texting, do you text? (yeah) oh em gee we have so much in common (said in joking tone) we should text, whats your number

Now obviously this is a pretty basic guide, but this style of setup is very noob friendly, it doesn't take a whole lot of calibration from beginning to end to get some decent results for ya.

hmmmm....
I'd thought of using this in conjunction with 60 years of challenge's 'milking the intro' technique... Basically, before you walk away, shake the girls' hand to thank her, and see if you get an IOI.
I don't think it shows low confidence, as the idea is to text the girls you get an IOI from 2 mins later to get an instant 'date', but:

I totally see your point:
1. It relies heavily on looks.
2. It's low probability and you've got to play the game of numbers.

I think I'm letting the romantic part of me get the better of my game too much though: I just thought, if you could pull this off, this would definitely make for a memorable experience for the target, and it'd be something she'd be telling her friends about... a bit silly, really.

Good idea but a girl might get really weirded out by this:

You: "Hey want to get coffee?"

Her: "Um who is this?"

You: "I'm the guy that asked to borrow your phone, called mine then sent you a text. Duh how else do you think I got your number ?"

Her: (calling 911).

I think this has more potential to go sour than not. Just my opinion.

Hey thanks for the feedback guys...

I'm gonna do it anyways just for the fun factor if it works, and will post a report on how it went when I get round to it.