lyam was telling us:
lyam nous racontait que :

Try this:
'_______________________________________
Dim rgeFind As Range

Set rgeFind = ActiveDocument.Range

With rgeFind.Find
   .ClearFormatting
   .Replacement.ClearFormatting
   .Text = "~~"
   .Replacement.Text = ""
   .Forward = True
   .Wrap = wdFindStop
   .Format = False
   .MatchCase = False
   .MatchWholeWord = False
   .MatchWildcards = False
   .MatchSoundsLike = False
   .MatchAllWordForms = False
   While .Execute
       NormalTemplate.AutoTextEntries("LISTNUM").Insert Where:=.Parent
       rgeFind.SetRange .Parent.End, ActiveDocument.Range.End
   Wend
End With

Application.Browser.Target = wdBrowsePage
'_______________________________________

I prefer using the Range object because the changes you make to Find and
Replace do not appear in the dialog box if you open it after running the
macro. When you use the Selection object, the Find/Replace parameters from
the code appear in the dialog box.

Also, you have to reset the Brower because Word thinks it is being helpful
by automatically setting the Browser to the last find you perform, even when
done by macro...

Jean-Guy Marcil was telling us:
Jean-Guy Marcil nous racontait que :

I saw the document you sent me, and as I surmised... you did not set up the
styles appropriately. ;-)

You need to start with the "Spacer" style.

Select it in the "Style and Formatting..." pane (Format menu). Choose to
modify it (Right click on its name in the list).

Go to Numbering (Format button), use one of the proposed Outline style
(under the Outline tab) and reset it to its default.

Next, choose to customize it.

Click on "More" to display the extra options.

Delete the content of the "Number Format" field.

At the bottom, select "Spacer" in the list of style in the drop down next to
"Link level to style".

Then back at the top, select the second level (The "2" under  "Level").

In the "Number Format" field make sure that the auto number "1" is followed
by a "." (Or what ever you want following the auto number).

At the bottom, select "Table Style Number" in the list of style in the drop
down next to "Link level to style".

Finally, make all the Number position and text position adjustments here
(not in the tab dialog or paragraph dialog).

After that you can set the font or other paragraph attributes as you would
with any other styles (Except for left position, the first tab and the left
indent).

Now you have a Level 2 outline that acts as a level 1.

Whenever handling Outline styles, this is the way to go. Create the
bare-bone styles first (no numbering), then start form the first level style
and create the outline form there. In the example above, if you had needed a
third or a fourth style in the outline, you would have modified it there.
All numbering must be handled from the first level style.

In your case, the Spacer style was not part of the Outline numbering
scheme,, so it had no impact.