As you say, @$row is an array; but I won't know what the element number is going to be from run to run.

You have a pretty deep misunderstanding of the code you are using. $table->rows() returns a list of arrays. Ie. $row is an array reference representing the fields (or columns) of each row of the table.

So whilst the position (row number) of the row containing the text Ships in port or not reporting today: will vary from run to run. The field or column within that row that contains the text will not.

I used the following code to dump all the tables from the url you posted in another thread to the screen, with '|' between each element of the rows:

#! perl -slw
use strict;
use LWP::Simple;
use HTML::TableExtract;

my $te = new HTML::TableExtract;
$te->parse( get( 'http://www.sailwx.info/shiptrack/cruiseships.phtml' 
+) );

for my $table ( $te->tables ) {
    print "\n-----------\n";
    for my $row ( $table->rows ) {
        local $^W;
        print join '|', @$row;
    }
}
[download]

Redirecting the output of that, junk | more, I got:

...
-----------

Ship|last reported (UTC)|position|Callsign
BATFR20|2008-Mar-20 2100|N 43░00', E 005░36'|BATFR20
BATFR21|2008-Mar-20 2100|N 41░36', E 008░24'|BATFR21
BATFR22|2008-Mar-20 2100|N 42░54', E 005░54'|BATFR22
...
Carribean Princess|2008-Mar-19 0600|N 19░18', W 065░18'|ZC
+DG8
Prinsendam|2008-Mar-19 0300|N 27░24', W 040░24'|PBGH
Ships in port or not reporting today:|||
TUSTUMENA|2008-Mar-18 1700|N 60░48', W 147░12'|WNGW
Oosterdam|2008-Mar-18 0800|N 23░00', W 107░48'|PBKH
...
[download]

From the empty fields on the end of Ships in port or not reporting today:|||, I can tell that the text that marks the transition from those ships at sea, to those in port, is returned in $row->[ 0 ].

So your test becomes:

...
for my $row ( $table->rows ) {
    if( $row->[ 0 ] ne 'Ships in port or not reporting today:' ) {
    ...
[download]