#!/bin/perl5
use strict;
use warnings;

open    ERRORFILE, ">>myprogram.error"
    or die "Can't open myprogram.error";
open    SAVEERR,   ">&STDERR";
open    STDERR,    ">&ERRORFILE";
select  STDERR; $| =1;

print   STDERR "stderr 1\n";

close   STDERR;
open    STDERR, ">&SAVEERR";

print   STDERR "stderr 2\n";