Yea. what Icefyre said. Remember. Shirou actually summons Saber to him on like 3 separate routes because she couldn't dematerialize and he wanted a relatively normal life so she stayed home while he went to school. She doesn't have Archer's range with Independent Action where he can be in an entirely different battlefield, but she doesn't need to keep by him.
Hell, there was a situation in Ataraxia. Where Shirou stayed behind on a bridge and Saber had to rush Archer on the top of a skyscraper at the edge of the city. And that was definitely more than a couple blocks away.
Edit:
There's also the fact that unlike shirou. Saber actually has a competent connection to varian in comparison to the shoddy connection Saber had to Shirou thanks to Illya knowing what the fuck she's doing. Remember, we saw her skill thanks to her being able to link Shirou's senses from a park bench in the middle of the city to a tree MILES away near the einzbern castle. Using a similar connection to the servant bond.