The Vatican Museums that include the Sistine Chapel have the classification in regards to dress codes as any other church or place of worship in Italy. So what to wear at the Vatican? When visiting the Vatican Museums in Rome all visitors males and females should wear as a minimum clothing that covers both their shoulders and knees.
So if you are visiting the Vatican in the hotter summer months, an applicable dress code for the Vatican would be a t-shirt and bermuda shorts that at least caste a shadow on your knees. As a sign of respect most visitors wear long-sleeve shirts and a pair of long pants.
For those visiting the Vatican who come unprepared, as a way to skip around the dress code of the Vatican you can purchase plastic cloaks that you can wrap around yourself to cover your knees and shoulders.
But, in the warmer summer months walking around in such a garment would not be very pleasant so plan ahead and pack accordingly so that you won't be disappointed on your travels in Italy.
Some people may think that the Vatican has very strict dress codes, but throughout Italy you will find many up-market restaurants and bars that won't allow customers to enter if they are not wearing long-pants and an appropriate shirt.