The Black Stars beat DR Congo 2-1 on Sunday to progress to the last four, thanks in every way to Andre Ayew's penalty following a foul on Christian Atsu.
The Indomitable Lions, on their part, secured a 5-4 shoot-out victory over pre-tournament favourites Senegal on Saturday, the two sides having played out a scoreless draw after extra-time.
“I saw the Cameroonians on Saturday and they were very good, a very tough side," Grant told Pulse Ghana.
"In the group stage, they played well and against Senegal, they were very impressive.
"Senegal created more chances but I think Cameroon deserved to win the match.
"The semi-final is going to be tough."
Ghana's fixture with Cameroon will be a repeat of their clash in 2008, when the two sides met in the semi-finals.
The Indomitable Lions ran out 1-0 victors, before falling to Egypt in the final.
Ghana, four-time Afcon winners, are hoping to win the tournament for the first time since 1982, having made the semis of the last five championships.