If tie is allowed, then combining theorbtwo's idea with an unorthodox tie seems to work: 
use strict;
use warnings;
$|++;
package NoStringify;
use Tie::Scalar;
use Carp;
our @ISA = ('Tie::StdScalar');
use overload q("") => sub { croak "Attempt to stringify reference" };

sub FETCH
{
    # return $self rather than $$self !
    my $self = shift;
}

package main;

my $var = 10;
my $ref = \$var;

tie $ref, 'NoStringify';

my $val = $$ref;
print "$val\n";
print $ref;

__END__
Output:

10
Attempt to stringify reference at ...

[download]

In reply to Re: How to prevent references from stringifying? by Arunbear
in thread How to prevent references from stringifying? by diotalevi

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