Similarly, for the original poster, Fill can do the job with an extra step of creating a bathub boundary around the raster and artificially altering the original DEM using the Con tool:
Before Fill tool (ocean on right):
After Fill tool:
Values behind the barrier are the lowest crossing point on the barrier.
You should be able to get to this using the Fill tool.
Hillshade Before:
Hillshade After Fill:
The values inside the filled sink are the elevation of the lowest point of the levee.
I am actually working on a project similar to this in respect to the needing to query the lowest "high" point on a ring levee.
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... I need the highest contour that completely crosses my rasters...
http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#//009z000000w7000000.htm for version 10 using the maximum option, however, every raster will be the zone and your contours will have to be grids if memory serves...a bit of a pain but check this out first and perhaps reformulate in light of this
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