Here's another alternative, not necessarily better or worse:
vb.net Code:
  1. Private Function GetStringLengthWithoutLineBreaks(text As String) As Integer
  2.     Return text.Split(New String() {ControlChars.NewLine,
  3.                                     ControlChars.Cr,
  4.                                     ControlChars.Lf},
  5.                       StringSplitOptions.None).Sum(Function(s) s.Length)
  6. End Function