I haven't used it myself, but I'd be inclined to look at something like Net::NTP to start with.  It's an interface to NTP, which is the "Network Time Protocol".

Update:  Using this as an excuse to try something new, I just installed Net::NTP from CPAN.

Here's an example based on the documentation:

use strict;
use warnings;
                                                                      
+          
use Data::Dumper;
use Net::NTP;
                                                                      
+          
my %response = get_ntp_response();
printf "NTP results => %s\n", Dumper(\%response);

__END__
NTP results => $VAR1 = {
          'Version Number' => 3,
          'Root Delay' => '0.129638671875',
          'Precision' => -16,
          'Leap Indicator' => 0,
          'Stratum' => 4,
          'Receive Timestamp' => '1179155054.2939',
          'Transmit Timestamp' => '1179155054.29393',
          'Reference Timestamp' => '1179154736.59929',
          'Originate Timestamp' => '1179155054.38672',
          'Poll Interval' => '0.0000',
          'Reference Clock Identifier' => '192.168.10.150',
          'Root Dispersion' => '0.0000',
          'Mode' => 4
        };
[download]

Maybe Net::NTP can help. If you go that route, it would also be useful to have a list of NTP servers.

Yes. See NIST Internet Time Service. In the US, NIST is, more or less by definition, the correct time, disregarding network latencies.