One way is to redirect stdout to a file. For this purpose it helps if the file is actually a Perl variable. Consider:

package Test_Package;

use strict;

sub testing {
   print "okay.";
};

1;

use strict;

use Test::More tests => 1;

my $log;

open my $logFile, '>', \$log;
my $oldStdOut = select $logFile;

Test_Package->testing();
select $oldStdOut;
close $logFile;

is($log, 'okay', 'Testing okay');
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Prints:

1..1
not ok 1 - Testing okay
#   Failed test 'Testing okay'
#   at ...\noname.pl line 25.
#          got: 'okay.'
#     expected: 'okay'
# Looks like you failed 1 test of 1.
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The error is deliberate btw.