eval {
  my $sender = Mail::Sender->new({on_errors => 'die', ...});
  $sender->Open({...});
  ...
  $sender->Close();
};
die "Failed to send the email: $@\n"
  if $@;

#or

my $sender = Mail::Sender->new({on_errors => 'undef', ...})
  or die "Failed to send the email: failed creating the object - $Mail::Sender::Error\n" 
$sender->Open({...})
  or die "Failed to send the email: $Mail::Sender::Error\n"
...
$sender->Close()
  or die "Failed to send the email: $Mail::Sender::Error\n";

#or
...