[Applescript to make application window active] The toggling of the visibility is necessary to deal with some weirdness that occurs with switching applications. If you don't toggle the visibility, the window won't be the first when you switch away from and back to the application. Unfortunately, this toggling shrinks the window to the dock then …

MakeWindowActive

to raiseWindow of theApplicationName for theName
    tell the application named theApplicationName
        activate
    set theWindow to the first item of ¬
        (get the windows whose name is theName)
    if index of theWindow is not 1 then
            set index to 1
            set visible to false
            set visible to true
        end if
    end tell
end raiseWindow

RaiseWindow2

to raiseWindow2 of theApplicationName for theName
    tell the application named theApplicationName
        activate
    set theWindow to the first item of ¬
        (get the windows whose name is theName)
        if the index of theWindow is not 1 then
            set the index of theWindow to 2
        tell application "System Events" to ¬
            tell application process theApplicationName to ¬
                keystroke "`" using command down
        end if
    end tell
end raiseWindow2