<div id="divResultados" runat="Server" visible="true">
       <asp:TextBox ID="firstName" runat="server"></asp:TextBox>
       <asp:TextBox ID="lastName" runat="server"></asp:TextBox>
       <asp:Calendar ID="calDOB" runat="server"></asp:Calendar>
           <asp:Button ID="Button1" runat="server" OnClientClick="return Message()" onclick="Button1_Click" Text="Button" />
    </div>

$(function(){
  $("#<%=Button1.ClientID%>").on("click", function(){
    $("#<%=calDOB.ClientID%>").hide();
  });
});

calDOB.Visible = false;