Process Explorer is an excellent replacement for the default Windows Task Manager. Process Explorer even automates this change via Options –> Replace Task Manager. However, by default, this won’t launch Process Explorer elevated. You can force it to run elevated by changing the registry (of course, the usual edit-the-registry-at-your-own-risk disclaimers apply).
HKLM\Software\Microsoft\Windows NT\CurrentVersion\Image File Execution Options\taskmgr.exe
append “/e” to the text for the value Debugger.
“<your path>\Procexp.exe” /e
If Process Explorer is running, close it explicitly via File –> Exit. Next time you launch it (which I always do via Ctrl-Shift-Esc), it will run elevated.