Just save both the key and the value each time you find a new maximum, instead of just the value. Something like this:

   # leave $vMax undefined initially so we don't need to
   # guess at the lowest value;  this also lets us know we
   # never actually looked for a maximum on the off-chance
   # that our hash is empty

   my ($kMax,$vMax);

   while(my ($k,$v) = each(%someHash)) {

      # if this is the first key,value pair, initialize $kMax,$vMax
      # otherwise only reset on a new maximum

      if (!defined($vMax) || ($v > $vMax)) {
         $kMax = $k;
         $vMax = $v;
      }
    }

    if (!defined($vMax)) {
      print "No entries in my hash table!\n";
    } else {
      print "key at maximum=$kMax, maximum value=$vMax\n";
    }
[download]