Here is some code I threw together quickly. It underlines words contained within quotation marks. The code could use a little work, though, so go ahead and make improvements as you see fit!
Code:
Sub Underline()
Dim idx As Long
Do While idx < ActiveDocument.Words.Count
idx = idx + 1
Select Case Trim(ActiveDocument.Words(idx))
Case Chr(147), Chr(148), Chr(34)
If Not ((idx + 2) > ActiveDocument.Words.Count) Then
Select Case Trim(ActiveDocument.Words(idx + 2))
Case Chr(147), Chr(148), Chr(34)
ActiveDocument.Words(idx + 1).Underline = wdUnderlineSingle
idx = idx + 1
End Select
End If
End Select
Loop
End Sub