Interpolating spatial data in contiguous sea areas only I have a dataset consisting of irregularly spaced points in the ocean. For each point I have coordinates and a data value.
I need to interpolate to a regular grid. So far, so easy.

There are areas of land within the area covered by the dataset, and in the original dataset there are simply no points there. I have polygons of the land boundaries.

I need to exclude the land from the output. This is fairly straightforwardly accomplished by checking which of the points on the target grid are within the polygons and removing them.
However, I also need to make sure that whatever interpolation technique is used does not consider points that are (for example) the other side of a peninsula - potentially a short distance away in a straight line, but a long way (or possibly not connected at all) by sea.

I'm sure that this must be a solved problem - I imagine any GIS package will have a way to deal with it - but I am at a loss as to what search terms to use in looking for the solution. 

I have been debating whether to ask this question here, or on stats.SE, or on GIS.SE, or on Stackoverflow... but let's see how it goes.
A very neat approach for optimal interpolation, which consider not only breaklines along the coast but also anisotropies caused by currents and horizontal diffusion, was given by Lynch &amp; McGillicuddy (2001). Their approach is quite elegant and takes advantage of the finite element methodology to avoid the transfer of information across boundaries.