Actually you have several problems in your code. Most likely the main issue is that back ticks returns a string so assigning the result to an array is unlikely to be meaningful. With that in mind the value being pushed doesn't make sense. On top of that your while loops should really be for loops to better convey the intent of the loops. So, consider:

use strict;
use warnings;

my @results;

for my $wibble (0 .. 4) {
    for my $wobble (0 .. 4) {
        my $result1 = `/home/devel/test1.ksh $wibble`;
        my $result2 = `/home/devel/test2.ksh $wibble`;
        push @{$results[$wibble][$wobble]}, "$result1;$result2";
    }
}
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Completely untested of course and I'm sure there are better names than wibble and wobble for the two loop counters that convey the sense of what the loops are fore, but I can't guess what they may be.