Java Ordered Map

In Java, Is there an object that acts like a Map for storing and accessing key/value pairs, but can return an ordered list of keys and an ordered list of values, such that the key and value lists are in the same order?

So as explanation-by-code, I’m looking for something that behaves like my fictitious OrderedMap:

OrderedMap<Integer, String> om = new OrderedMap<>();
om.put(0, "Zero");
om.put(7, "Seven");

String o = om.get(7); // o is "Seven"
List<Integer> keys = om.getKeys();
List<String> values = om.getValues();

for(int i = 0; i < keys.size(); i++)
{
    Integer key = keys.get(i);
    String value = values.get(i);
    Assert(om.get(key) == value);
}