Try this:
<asp:UpdatePanel ID="gt" runat="server" UpdateMode="Conditional">
<Triggers>
<asp:AsyncPostBackTrigger ControlID="BtnEnquirySend" />
</Triggers>
<ContentTemplate>
<asp:Button ID="BtnEnquirySend" runat="server" Text="Send" style=" left:910px; top:845px; position:absolute;" OnClick="BtnSend_Click" />
<asp:Panel ID="Panel11" runat="server" style=" height:300px; width:200px; margin-left:170px; margin-top:400px">
<asp:Label ID="Label3" runat="server" Text="Check"></asp:Label>
</asp:Panel>
<asp:ModalPopupExtender ID="MPE" runat="server"
TargetControlID="BtnEnquirySend"
PopupControlID="Panel11"
BackgroundCssClass="modalBackground"
DropShadow="true">
</asp:ModalPopupExtender>
</ContentTemplate>
</asp:UpdatePanel>
The panel has no values.That's why it looks like not showing.