You can take a functional approach and chain grep and map on a single line:

#! perl
use strict;
use warnings;
use Data::Dump;

my %h1 = (catastrophe => 1, cataclysm => 2, dogma => 3);
my %h2 = map { $_ => $h1{$_} } grep { /^cat/ } keys %h1;
dd %h2;
[download]

Output:

 1:33 >perl 542_SoPW.pl
("catastrophe", 1, "cataclysm", 2)

 1:37 >
[download]

Hope that helps,