Kompany, 25, has missed City's last four matches after picking up a controversial red card in his side's FA Cup defeat against rivals Manchester United.
City have won both of their Premier League matches in his absence but the Belgian has seen his side dumped out of the Carling Cup over two legs by Liverpool.
Kompany is poised to make his comeback on Tuesday night for the table-toppers' trip to Everton, and Richards is eagerly looking forward to lining up alongside the commanding centre-back.
Richards said: "He has been an unbelievable miss. He is our captain and he and Joleon (Lescott) have been our best central defensive partnership this season.
"He has played well in the big games and is a leader so it will be amazing to have him back and we can't wait to play with him again.
"He has still been coming in the changing room before games and saying how he feels we can improve, and what he would do if he was on the pitch, so he has still been an influence.
"But it's not nice for anyone. All the players and staff wanted him to play and he was kicking himself because it was another harsh decision to give him the ban. I am sure when he comes back he will give 110% and help us back to winning ways."