Maps have a sort() method, just like lists. They even use the same default comparator function. To preserve the order of the map after sort() has been called, you can use toOrderedMap() to convert it, as follows:

const myMap = Map.of(
  'three', 3,
  'one', 1,
  'four', 4,
  'two', 2
);
const mySortedMap = myMap
  .toOrderedMap()
  .sort();

myMap.forEach(
  (v, k) => console.log('myMap', `${k} => ${v}`)
);
// -> myMap three => 3
// -> myMap one => 1
// -> myMap four => 4
// -> myMap two => 2

mySortedMap.forEach(
  (v, k) => console.log('mySortedMap', `${k} => ${v}`)
);
// -> mySortedMap one => 1
// -> mySortedMap two => 2
// -> mySortedMap three => 3
// -> mySortedMap four => 4

The semantics of sort() are the same for lists and maps, as you can see by the sorted output. The iteration order of mySortedMap will always be the same, because it's an OrderedMap. When the sort happens, a new ordered map is created with the values in the expected order and an internal index to guarantee iteration order.