The Spireites make the short trip to the Don Valley Stadium on Saturday looking to extend their seven-match unbeaten run, and Richardson is expecting a stern test.
"For me, Rotherham are as good as anybody in this division so it is going to be a very tough game," he said.
"Had it not been for the 17-point deduction that they had at the start of the season then they would be firmly in the play-offs. They had a good cup run as well and they have had a very good season.
"It is a game against our local rivals and it is a game that we are very much looking forward to."