A similar way but utilizing Regular Expressions built in features:

vb Code:
  1. Private Function GetMyIP() As IPAddress
  2.         Dim outputIP As IPAddress
  3.         Using wClient As New WebClient
  4.             Dim myIP As String = Regex.Match(wClient.DownloadString("http://www.ip-adress.com/"), "(?<=<h2>My IP address is: )[0-9.]*?(?=</h2>)", RegexOptions.Compiled).Value
  5.             outputIP = IPAddress.Parse(myIP)
  6.         End Using
  7.         Return outputIP
  8.     End Function

Or if you want to get ugly

vb Code:
  1. Private Function GetMyIP() As IPAddress
  2.         Using wClient As New WebClient
  3.             Return IPAddress.Parse(Regex.Match(wClient.DownloadString("http://www.ip-adress.com/"), "(?<=<h2>My IP address is: )[0-9.]*?(?=</h2>)", RegexOptions.Compiled).Value)
  4.         End Using
  5.     End Function