The basic value would be the number of bits set. You can add weight to certain bits, or to certain fields, or to both.
Terribly under-tested code:

use strict;
use warnings;
my %match = (
    'ABC.com' => {
        'XYZ.com' => {
            company => 1,  # reg. only
            contact => 0,  # no match
            address => 3,  # reg. and admin.
            phone   => 2,  # admin. only
            email   => 2,  # admin. only
        },
        'BBC.com' => {
            company => 3,
            contact => 3,
            address => 3,
            phone   => 3,
            email   => 3,
        },
    },
    
    'FOO.com' => {
        'BAR.com' => {
            company => 1,
            contact => 3,
            address => 3,
            phone   => 2,
            email   => 1,
        },
        'BAZ.com' => {
            company => 3,
            contact => 2,
            address => 2,
            phone   => 2,
            email   => 2,
        },
    },
);

# I'm sure there is a faster way to count bits.
sub bit_count {
    my ( $number ) = @_;
    my $bits = unpack 'b*', pack 'C', $number;
    my $bits_set = ( $bits =~ tr/1// );
    return $bits_set;
}

sub confidence_by_bits {
    my ( $href ) = @_;

    my $weight = 0;
    foreach ( values %{ $href } ) {
        $weight += bit_count($_);
    }

    return $weight;
}

sub confidence_by_weighted_position {
    my ( $href ) = @_;

    my $weight = 0;
    foreach ( values %{ $href } ) {
        # Reg - slightly important
        if ( $_ | 1 ) {
            $weight += 1;
        }
        # Admin - very important
        if ( $_ | 2 ) {
            $weight += 5;
        }
        # Bonus for both
        if ( $_ == 3 ) {
            $weight += 20;
        }
    }

    return $weight;
}

sub confidence_by_weighted_field {
    my ( $href ) = @_;

    my $weight = 0;
    while ( my ( $key, $val ) = each %{ $href } ) {
        my $bits = bit_count($val);
        if    ( $key eq 'company' ) {
            $bits *= 5;
        }
        elsif ( $key eq 'phone' ) {
            $bits *= 0.8;
        }
        $weight += $bits;
    }

    return $weight;
}


print_with_confidence( \%match, \&confidence_by_bits              );
print_with_confidence( \%match, \&confidence_by_weighted_position );
print_with_confidence( \%match, \&confidence_by_weighted_field    );

sub print_with_confidence {
    my ( $match_href, $conf_func ) = @_;
    while     ( my ( $domain1, $v1 ) = each %match ) {
        my @candidates;
        while ( my ( $domain2, $v2 ) = each %$v1 ) {
            my $confidence = $conf_func->( $v2 );
            push @candidates, [ $domain2, $confidence ];
        }
        @candidates = sort {
            $b->[1] <=> $a->[1] ||
            $b->[0] cmp $a->[0]
        } @candidates;
    
        print "$domain1\n";
        foreach ( @candidates ) {
            my ( $domain2, $confidence ) = @{ $_ };
            printf "\t%7d\t%s\n", $confidence, $domain2;
        }
    }
    print "\n";
}
[download]

Output:

ABC.com
             10 BBC.com
              5 XYZ.com
FOO.com
              7 BAR.com
              6 BAZ.com

ABC.com
            130 BBC.com
             50 XYZ.com
FOO.com
             70 BAR.com
             50 BAZ.com

ABC.com
             17 BBC.com
              8 XYZ.com
FOO.com
             13 BAZ.com
             10 BAR.com
[download]