For some value of "better" (untested):

use warnings;
use strict;
use POSIX qw(strftime);

my $logsIncDate     = strftime('%b %d %H', localtime);
my $TimeStamp       = strftime('%Y%m%d'  , localtime);
my $logFile         = "/home/log.$TimeStamp";
my $sendmailPath    = '/usr/lib/sendmail myemail@bng.org';
my $subject         = 'Subject: Emyemail@crf.org';
my $from            = 'From: myemail@bng.org';

##### grep through switch logs and if-found send e-mail
my @err;
open SwitchLogs, '<', $logFile or die "Could not open $logFile: $!"; 
while (<SwitchLogs>) {
    push @err, $_ if /$logsIncDate/ && /PM-4-ERR_DISABLE/;
}
close SwitchLogs;

if (@err) {
    open(SENDMAIL, "|$sendmailPath") or die "Cannot open $sendmailPath
+: $!";
    print SENDMAIL <<EOF;
$from
$subject
$to
Content-type: text/plain


Log messages:

@err;

EOF
    close(SENDMAIL);
}
[download]

Note: you don't set $to

Update: due to NetWallah