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I have created a series of DEMs that layercake on top of each other.

I would like to be able to lookup a coordinate and get the elevation that has already been interpolated. The goal is to introduce a new data point (coordinate and elevation) and determine which layer of the cake the new point is closest to.

I am using QGIS.

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You could use the Point Sampling Plugin. This can handle multiple points in the input file. In the output you will have a series of fields named after your raster layers (the names may be truncated). You can then compare your point elevation to the values in the fields and perhaps create a new field populated via a conditional expression that finds the nearest match and gives a value to each point that identifies the relevant DEM layer.

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