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
... I need the highest contour that completely crosses my rasters...
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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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.
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.