I have a tune that I like to play that sounds really cool if one of the C naturals in it is bent up just shy of a C#. What is the best way to do that?
You talkin’ about trying for that upward-bendy Nyaah thing that uilleann pipers do? If so, here’s what I do as it works on my flute:
OXX XXO
OXX OOO
OXO OOO
The transition from one to the next is the same as when you’d upslide any other note; you have to finesse it with your fingers. I usually start by lifting the tip and letting the rest of the finger follow in a chain reaction, curving up and away, and in this case each position morphing smoothly into the next. It ain’t easy to make perfect, and it’s not as much a stand-out effect as on the pipes, but it does the job.
Basically a C subnatural to C supernatural.
But this might be good enough for your purposes, too:
OXX OOO (depending on how you crossfinger your Cnat)
OXO OOO
Some folks are more comfortable halfholing this stuff.
Hey thanks. That second one might do the trick. It’s not easy to do.
I actually heard this on fiddle, but I guess the “nyah” thing is what it is.
I do something similar to what Nano posted with a few differences (apart from fingering differences that are inconsequential):
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I lip down (blowing more into the hole) to flatten the C at the beginning of the note – this accentuates the effect.
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When I shift toward the C supernatural, like Nano I slide the fingers of my top hand off rather than just lifting them. But I also lip back up, so you get a very smooth transition from a flat C to almost a C-sharp.
Lipping! Good idea, and an embarrassingly obvious one, but for the life of me I don’t know if I’ve been doing it or not in this case. If I have, it’s been instinctive. If I haven’t, I do believe I’ll start, or at least be more aware of its uses. A whole extra range of nuance to be had there. 
Oh yeah, and by the way: the fingering end of my way of doing it presupposes the so-called “piper’s” grip. If you’re a Rockstro-type fingertip gripster, maybe lipping is the supreme way to go? Makes sense, anyway.
Which tune were you referring to, actually?
Boy it all sounds a bit complicated to me or maybe I’m not understanding the question. To slide up to C# I just go from xoo ooo and slowly roll the finger off. If you don’t want to start from the B (say Cnat) I still do the same thing - just do the first part of the slide quicker and the B part of the operation is almost unnoticale. I guess going beyond C# is where it gets dicey, but I would be inclinded to then lip it up from there. Can’t think of a time when I’ve wanted to do that, however.
Clark
Lotsa ways to skin that cat.
I’ll go for the C-ish upslide when I specifically want to emulate that pipey “Nyaah” effect, which isn’t all so very often. A fluter could overdo that sort of thing.