South Africa have qualified for the last four with six wins and two losses in eight games while Afghanistan, their opponents in Ahmedabad on Friday, still harbour outside hopes of squeezing into the semi-finals.
"They've been really, really good to watch," said Miller of Afghanistan who have beaten defending champions England as well as former winners, Pakistan and Sri Lanka.
They were in touching distance of another major scalp on Tuesday when they had five-time champions Australia on the ropes before Glenn Maxwell launched his spectacular one-man rescue mission.
"They're a team that's certainly growing in confidence. They've shown that they can compete. I mean this World Cup they've done really, really well, beaten some big teams."
He added: "It's been good to watch the Afghanistan group going the way that they have with the spinners that they've got, the batters up front.
"They have a chance to make the semifinals. That's the joy of the World Cup. You see different teams doing well, people that don't necessarily rate a certain team exceeding in a certain phase of the World Cup."
Miller hailed Maxwell's undefeated 201-run masterclass, achieved despite cramps and back spasms which forced him to attempt only boundaries as he pulled his team back from the brink of 91-7 in Mumbai on Tuesday.
"Seeing a knock like that was really special," said Miller of Maxwell who he will face again in the semi-finals next week.
"He's an X-Factor, a match winner. It was inspiring to see no foot movement there and still hitting sixes and fours. From a game where they were dead and buried."
Miller admitted players were excited at the prospect of a World Cup semi-final against Australia.
When they met in the group stage at Lucknow four weeks ago, Maxwell was out for three and South Africa romped to a 134-run victory.
"We played them before in the World Cup, so kind of a dress rehearsal there and we've played them quite a bit in the past," said Miller of the five-match home series on the eve of the World Cup that South Africa won 3-2.
"So, we know what to expect. They're always a competitive team. They've got some incredible players and match winners amongst their team."