[c#] How to call window.alert("message"); from C#?

It's a bit hard to give a definitive answer without a bit more information, but one usual way is to register a startup script:

try
{
  ...
}
catch(ApplicationException ex){
  Page.ClientScript.RegisterStartupScript(this.GetType(),"ErrorAlert","alert('Some text here - maybe ex.Message');",true);
}