Creo il WebUserControl nella directory App_Code come da esempio (ha solo una proprietà pubblica)
codice:
Public Class WebUserControl1
    Inherits System.Web.UI.UserControl

    Private _Nome As String = ""
    Public Property Nome() As String
        Get
            Return Me._Nome
        End Get
        Set(ByVal value As String)
            Me._Nome = value
        End Set
    End Property

End Class
Creo in una qualunque directory il WebUserControl che eredita dal primo

codice:
<%@ Control Language="VB" AutoEventWireup="false" CodeFile="WebUserControl.ascx.vb" Inherits="prove_WebUserControl" %>
codice:
Option Strict On
Imports l = libreria.ModuloWeb

Partial Class prove_WebUserControl
    Inherits WebUserControl1

    Private _Cognome As String = ""
    Public Property Cognome() As String
        Get
            Return Me._Cognome
        End Get
        Set(ByVal value As String)
            Me._Cognome = value
        End Set
    End Property

End Class
ho aggiunto la proprità Cognome.
Questa classe eredita pure la proprietà Nome

La pagina di collaudo
codice:
<%@ Page Language="VB" AutoEventWireup="false" CodeFile="a.aspx.vb" Inherits="prove_a" %>

<%@ Register src="WebUserControl.ascx" tagname="WebUserControl" tagprefix="uc1" %>

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">

<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
    <title></title>
</head>
<body>
    <form id="form1" runat="server">
    <div>
        <uc1:WebUserControl ID="WebUserControl1" runat="server" Nome="Pinco" Cognome="Pallino" />
    </div>
    </form>
</body>
</html>
codice:
Option Strict On
Imports l = libreria.ModuloWeb

Partial Class prove_a
    Inherits System.Web.UI.Page

    Protected Sub Page_Load(ByVal sender As Object, ByVal e As System.EventArgs) Handles Me.Load
        l.PrintLn(Me.WebUserControl1.Nome & " " & Me.WebUserControl1.Cognome)
    End Sub
End Class

ps. :master: a che serve un UserControl non visuale? (mai visto un esempio in giro)