You can get a more customizable effect via %SIG handlers. A quick proof-of-concept:

use IO::Handle;
my $filename = "/etc/passwd";
open my $fh, '<', $filename or die $!;
my $customerr = sub {
    my $msg = shift;
    $msg =~ s/\.?\s*$//;
    return "$msg ($filename line ".$fh->input_line_number.")\n";
};
local $SIG{__WARN__} = sub { warn $customerr->(shift) };
local $SIG{__DIE__} = sub { die $customerr->(shift) };
while (<$fh>) {
    warn "BEEP!" if /root/;
    die "ACK!" if /nobody/;
}
close $fh;
__END__
BEEP! at - line 12, <$fh> line 1 (/etc/passwd line 1)
ACK! at - line 13, <$fh> line 7 (/etc/passwd line 7)
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It may be a little more work than using Perl's built-in mechanisms, but it works great in other cases too - for example if you're going over the rows of a spreadsheet, you can include the row number in the error message.