Explanation:

- Original sentence: Last week he promised that he would have come today, but he hasn’t arrived yet.

- Option 1: No improvement.

- The original phrase "that he would have come" implies an action planned for the past, but the situation is about a future action based on a past promise.

- Option 2: "that he will have come"

- Implies completion by a future time, does not align with the intended promise for today.

- Option 3: "that he will be coming"

- Implies ongoing or continuous action; unnecessary complexity for the context.

- Option 4: "that he would come"

- Matches the context of a promise made in the past about a future action. It conveys the correct sense of intention from a past perspective.

Therefore, the best option is Option 4: "that he would come".