When you get new windows, you won't need to get new window coverings if you don't want to, but you should get new screens. Screens have limited life spans, too, even if they continue to look all right for a long time. Replacing the screens gives your windows a completely fresh start and enables the windows to look better for a longer time.
Replace Brittle Mesh
The screen material can be metal or plastic, but in either case, the material can become brittle after several years of exposure to sun, heat, cold, rain, and ice, depending on where you live. New screen material can still be fragile, but you'd have to actively poke at it to get it to tear. With an older screen, just brushing against the mesh can break a few strands if the condition has deteriorated enough.
Screen mesh is pretty dark to begin with, but after years of use, it becomes laden with grime. The dark look is more grungy in this case. Adding new screens means all that grime is gone, and your windows look a little cleaner when you view them from outside the house. Plus, if there's a driving rainstorm with water droplets slamming into the screen and window, there will be less grime that can transfer onto the window glass itself.
Restringing Can Warp Screen Frame
One option you might have considered as an alternative is restringing, or adding new mesh to the old frame. Not only does this take longer to do, but restringing can pull part of the screen frame in, warping the shape as a whole. You may as well just buy another screen that's completely new in that case. Restringing can be a bit cheaper sometimes, but considering the side effects it can have, it might not really save you money in the end. Completely new screens still win out.
If your current screens are very old, chances are the newer screens will have better-quality materials that are more durable. Technology marches forward for pretty much anything, including window screens, so take advantage of improved manufacturing and get new screens.
The window company who is replacing the glass should have screens in stock that perfectly fit the window models the company uses. You may be able to get screens as part of a package with the windows, too, so ask about any deals that are going on. Click here to learn more about window replacement.