I have a series of control points with xy coordinates in both NAD83 UTM and in a local grid.
How can I go about creating a new projection file in ArcGIS 10 for the local grid?
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This ESRI support article - "Create a custom projection file with units of feet or meters in ArcMap" tells you how to do it. It claims to be for ArcGIS <10, but I don't see anything obvious that makes it incompatible with 10.
Create Custom Geographic Transformation (Data Management)
"Creates a transformation method for converting data between two geographic coordinate systems or datums. The output of this tool can be used as a transformation method for any tool with a parameter that requires a geographic transformation."
Note: All custom geographic transformation files are saved with a .gtf extension and stored in the ESRI\\ArcToolbox\CustomTransformations folder under the user's Application Data folder. The CustomTransformations folder is created by the tool if it does not exist. If the Application Data folder is read-only or hidden, the output is created in ArcToolbox\CustomTransformations under the user's temp folder. The location or name of the Application Data and temp folders is dependent on the operating system.