The aforementioned methods will work great if you want to redirect STDERR to a file. However, if you want to redirect it to a file AND still display it on the STDERR device (e.g. the screen) you might try Filter::Handle. It will let you attach a sub to a file handle (including STDERR) so that you can print the output to a file or filter it any way you like in addition to printing to the terminal. Here's a little snippet to get you started.

use warnings;
use strict;
use Filter::Handle qw/subs/;

open (LOGFILE, ">logfile") || die "could not open logfile";

#filter STDERR through an anonymous sub
Filter \*STDERR, sub {local $_ = "@_"; print LOGFILE "Filtered: $_ "; 
+$_};

#prints to both STDERR and to LOGFILE
print STDERR "error!\n";

#STDERR will no longer be filtered through your sub
UnFilter \*STDERR;

close LOGFILE;
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Regards,
Rhet