open(LOG,"< test_small.xml") or die "Unable to open logfile:$!\n";

my $count = 0; # Initialise a count variable to 0.
while(<LOG>) {
    my $line = $_;
    if ($line =~ m/^> PORTZONESHOW/../^> */) { # Did you mean 2 dots here instead of 3?
        if ( $line =~ m/^PORT:/) {
            $count++; # Increment it everytime you find a match.
            print $line;
        }
    }
}

close LOG; # Its a good practice to close file handles yourself.
print "Count: $count\n"; # Print $count