How about this compared to your methods? How are you comparing the speeds?

Function removeDuplicates(ByVal initialArray As String()) As String()
Dim i As Integer = 0
Dim j As Integer = 0
Dim newArray(0) As String

For i = 0 To UBound(initialArray)
For j = 0 To UBound(initialArray)
If Not initialArray(i) = "" Then
If Not j = i Then
If initialArray(i) = initialArray(j) Then
initialArray(j) = ""
End If
End If
End If
Next
Next

j = 0
For i = 0 To UBound(initialArray)
If Not initialArray(i) = "" Then
ReDim Preserve newArray(j)
newArray(j) = initialArray(i)
j = j + 1
End If
Next

Return newArray

End Function