Yes, a 99% C.I will be wider than a 95% C.I.

Just think of it in terms of a critical value from some probability distribution e.g. standard normal.

For example we could have XBar = 100 with a standard error of 10. Thus, the 95% C.I. would be

100 + - 1.96* 10.

The 99% C.I. would be

100 + - 2.58*10

obviously making it wider than the 95% C.I.