1)"The test results didn't come through before we went home."
2)"The test results came throuogh after we went home."
Which one would be more natural?
Sentence 2 makes it clear that the test results came through at some point (in this case, after we went home).
Sentence 1 gives no indication as to whether the test results have come through. It simply states that they hadn't come through by the time we had to go home. Perhaps they came through after. Perhaps they didn't.