Here’s a little Gaussian process emulator example that I cooked up using the R package DiceKriging.
The function is Higdon02, from this useful archive on simulation experiments. I’ve used a constant to initiate the model fit on the smallest data set:
km(form=~1, ...)
rather than a linear term:
km(form=~., ...)
as otherwise you end up with a horrible emulator:
Interestingly, even that problem goes away if you add enough data points.
Doug McNeall's blog 
GPs are nice (but R isn’t ;o). I use one for my sea ice extent predictor (this is an old image)
Error bars that get wider as you move away from the data are very sensible (but ideally they ought to include the uncertainty in estimating the parameters of the covariance function).
That’s nice – Matlab? Python? I’ve got a time series version that my college Andrew coded up in RJAGS, which I think includes the hyper parameter uncertainty too.
College? Colleague.
It is MATLAB, using the excellent GPML toolbox
http://www.gaussianprocess.org/gpml/
It isn’t a serious attempt to predict Arctic sea ice, I was mostly just experimenting with the toolbox, but it has done reasonably well over the last few years.
There is another good MATLAB toolbox called GPstuff
http://research.cs.aalto.fi/pml/software/gpstuff/
but I haven’t used it very much (yet).