If your files are not too large, toolic's solution might be faster if you read in the entire file at one time into an array and loop through the array:

my @fileData = <FILE>;
foreach my $fileLine (@fileData) {
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Also, if you don't mind using unix grep, you can still use it and do post-processing, by opening the grep as a pipe:

open (DATA, "grep <string> <file-list> |");
while (<DATA>) {
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