You are assuming it always matches (or else you'd get a warning), so I'm going to rely on that same assumption.

($num) = $num =~ /2(0\d)/;
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Without the assumption:

$num = $num =~ /2(0\d)/ ? $1 : undef;
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An alternate solution:

(...) = map sprintf('%02d', $_), ...
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$num =~ s/.*?20(\d).*/0$1/gs
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Since \d always matches one digit, the sprintf is not really needed.

Note that $num =~ /20(\d)/ returns in list context the matches, and an empty list when there are none. So if you need to check whether a match occured, you can't do that here. However, you can provide to sprintf a default value, since it only uses the values it needs, and if there's an extra one it's ignored:

sprintf("%02d", ($num =~ /20(\d)/), 0);

A general example: print sprintf("%s\n", (/(bar)/), 'default') for qw(foo bar)

Another method, from the unnecessary ternary operator dept:

$output = (/20(\d)/ ? sprintf("%02d", $1) : format_error("that isn't valid data!"));

Actually you want $num = sprintf("%02d", $num % 100); to avoid Y2K errors.

; separates statements. Putting two statements onto the same line does not make them a single statement any more than writing this as

($num)
 = 
$num
 =~ 
m#20(\d)#;
($num)
 = 
sprintf(
 "%02d",
 $num
);
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makes it 11 statements.

I anyway liked his take on the question!
Anonymous Monk++;
;-)