Ho risolto così.... 
Private Sub GetFiles()
Dim di As New DirectoryInfo(Server.MapPath("~/File"))
If di.Exists Then
GridView2.DataSource = di.GetFiles("*" & Me.TextBox1.Text & "*")
GridView2.DataBind()
End If
End Sub
Protected Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click
Me.GetFiles()
End Sub
Grazie. Un saluto.