Interestingly, bing is the one which fails for me:

$ cat ssl.t
use strict;
use warnings;

use Test::More;
use LWP::UserAgent;

my @hostnames = (
    'google.com',
    'microsoft.com',
    'bing.com'
);

plan tests => 1 + scalar @hostnames;

cmp_ok ($LWP::UserAgent::VERSION, '>=', 6.04, 'LWP is at least fairly 
+recent');
my $ua = LWP::UserAgent->new;
for my $host (@hostnames) {
    my $res = $ua->head ("https://$host/");
    is ($res->code, '200', "$host returns 200")
}
$ prove -v ssl.t
ssl.t .. 
1..4
ok 1 - LWP is at least fairly recent
ok 2 - google.com returns 200
ok 3 - microsoft.com returns 200
not ok 4 - bing.com returns 200

#   Failed test 'bing.com returns 200'
#   at ssl.t line 19.
#          got: '405'
#     expected: '200'
# Looks like you failed 1 test of 4.
Dubious, test returned 1 (wstat 256, 0x100)
Failed 1/4 subtests 

Test Summary Report
-------------------
ssl.t (Wstat: 256 Tests: 4 Failed: 1)
  Failed test:  4
  Non-zero exit status: 1
Files=1, Tests=4,  2 wallclock secs ( 0.04 usr  0.02 sys +  0.33 cusr 
+ 0.02 csys =  0.41 CPU)
Result: FAIL

[download]

405 is "Method Not Allowed" so bing is just disallowing HEAD requests. I am unable to reproduce your errors and am interested to see your code which works in successfully retrieving a response to a HEAD from bing.com.

Addendum: here are the relevant version numbers:

In reply to Re: Error 500 in LWP by hippo
in thread Error 500 in LWP by YarNik

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