Any ideas about how I might do this?

Here's one way...

#!/usr/bin/perl -w
use Tie::File;
use strict;

my @ry=();
tie @ry,"Tie::File","mybigfile" or die "mybigfile:$!";
@ry = grep /mypattern/,@ry;
untie @ry;
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Please note: that was off the top of my head and untested.