I wasn't sure which wiki to put this in.  If the moderator has a better idea, please move it. 

First, let me say norton ghost will do this easily, but not everyone has access to it.

tools used:  bootable WinPE flash drive and imagex.exe from Microsoft AIK.
free tool mkbt.exe from http://www.nu2.nu/mkbt

Background:  The Dell diagnostic utility partition is a special hidden partition typically found at the beginning of hard drives shipped from Dell.  You can boot it using F12 option.  This partition is a FAT formatted partition with a custom type id of "DE" instead of "06".  The OS on this partition is a dell modified DOS.  To make a DOS partition bootable you use the SYS command, but there is no SYS command (that I know of) for the customized Dell DOS.  Instead I use imagex to clone the partition file data, and mkbt to binary clone the boot sector.  NOTE: I said boot sector, not the mbr.

The target drive number will be referred to as Y and the target diagnostic partition number will be referred to as Z.  Typically Y=0 and Z=1.  The target diagnostic partition drive letter will be referred to as D: and the flash drive letter will be referred to as F:.  These almost certainly will be different on your system.
Use diskpart commands:
list disk
list part
list vol
to verify this.

First to make the backup clone:
boot WinPE
diskpart
list disk
select disk Y
list part
; note: You are looking for the OEM partition.  Remember the size of it.
select part Z
assign
list vol
exit
; note: you may want to copy mkbt.exe to D: now
mkbt.exe -x -c D: D:\dellboot.bin
imagex /capture D:\ F:\delldiag.wim "DellDiag" "Dell Diagnostics Utility Partition" /check /verify
exit

Second, prepare the target disk
boot WinPE
diskpart
select disk Y
clean  * WARNING: this optional step destroys data and builds a new empty MBR
create partition primary size=99 id=de
format fs=fat label="DellDiag"
assign
list vol
exit

Third, restore the clone
... (continued from step 2 without rebooting)
imagex /apply F:\delldiag.wim 1 D:\ /check /verify
mkbt -x D:\dellboot.bin D:
exit