Seven-time Cincinnati champion Federer will meet Goffin not before 19:00 local time (00:00 BST).
On his win over Goffin, the game ended at 7-6, 1-1, Federer added: "I think I played pretty good in that first set but we could see that David was struggling with the shoulder".
"It's quite unusual to stop for lightning", Federer said after beating Wawrinka for the 23rd time in 26 meetings.
"I'm not proud when I break the racket, especially I know there are kids around and watching and I'm not proud of it", he said.
The Swiss was not distressed to get a quick win.
"But all of that is not going to happen if I lose so I'll try everything I can and hope for the best".
Halep had twice staged fightbacks earlier in the match, initially coming from a set down before rallying again from 3-0 behind in the decider. He got better as the rainy week went on in Cincinnati, playing his best at the end.
Djokovic leads in head-to-head title matches 11-6 and the overall series 23-22.
Federer won their only previous final here in 2015 in straight sets.
"I can not find words for this moment", she said. "I have plenty of motivation". Now, it's on to his first Cincinnati final in three years.
"Hopefully I can get it done this time".
Djokovic had to work for more than two and a half hours to overcome Cilic, the 2016 champion in the combined WTA and ATP event.
Djokovic only secured his defeat of the Croatian late in the final set, breaking for 5-3 and finishing off the hard-fought victory in the next game.
"It's been a rollercoaster week with matches, interruptions, and rain delays and everything", Djokovic said.
Djokovic, a five-time finalist in Cincinnati, is aiming to lift the trophy at the sole Masters 1,000 series event he has never won. Firing 12 aces and having nearly half of his serves unreturned, the Swiss won his 11th consecutive match in Cincinnati.
"I feel like I'm trying to defend my title from way back when", he said.
Despite those exertions, the veteran compatriots produced a display of impressive consistency, with no breaks in either of the first two sets, and some exquisite shot-making on show, particularly from the backhand of Wawrinka.
"I'm feeling great, I'm so happy to win", she said after advancing on her first match point as Kvitova slammed a forehand into the net. "I haven't played any matches on the centre court".
She will face rising 20-year-old Aryna Sabalenka of Belarus, who upset Madison Keys of the United States 6-3 6-4. The second set was more straightforward, as Cilic never faced a break point on his way to claiming victory in 1 hour, 45 minutes.