Karen measured her height as 59 inches. That is 27 inches more than half her older sister's height. How tall is her older sister?

Let's say Karen's older sister's height is H inches.

Half her older sister's height is H/2 inches.
Karen's height is 59 inches, which is 27 inches more than half her older sister's height, so H/2 + 27 = 59
H/2 = 59 - 27
H/2 = 32
H = 32 * 2
H = <<64=64>>64
Karen's older sister is 64 inches tall. Answer: \boxed{64}.