Try Net::SSLeay on for size :)
#!/usr/bin/perl --
use LWP::Simple ;
use IO::Socket::SSL qw(debug3);
get( q{https://pilot-payflowpro.paypal.com/} );
__END__
DEBUG: .../IO/Socket/SSL.pm:1567: new ctx 18240320
DEBUG: .../IO/Socket/SSL.pm:334: socket not yet connected
DEBUG: .../IO/Socket/SSL.pm:336: socket connected
DEBUG: .../IO/Socket/SSL.pm:354: ssl handshake not started
DEBUG: .../IO/Socket/SSL.pm:1555: ok=1 cert=18273264
DEBUG: .../IO/Socket/SSL.pm:1555: ok=1 cert=18997536
DEBUG: .../IO/Socket/SSL.pm:1555: ok=1 cert=18245888
DEBUG: .../IO/Socket/SSL.pm:1170: scheme=www cert=18245888
DEBUG: .../IO/Socket/SSL.pm:1177: identity=pilot-payflowpro.paypal.com
+ cn=pilot-payflowpro.paypal.com alt=2 pilot-payflowpro.paypal.com
DEBUG: .../IO/Socket/SSL.pm:414: Net::SSLeay::connect -> 1
DEBUG: .../IO/Socket/SSL.pm:469: ssl handshake done
DEBUG: .../IO/Socket/SSL.pm:1604: free ctx 18240320 open=18240320
DEBUG: .../IO/Socket/SSL.pm:1609: free ctx 18240320 callback
DEBUG: .../IO/Socket/SSL.pm:1612: OK free ctx 18240320