Mos t print labs have profiles they will provide to you so you can soft proof your images before you send them to the lab. Softproofing will help you visualize the relationship between what you are seeing on your calibrated and profiled display and what you should expect from the print lab as print output. Then you send some test prints off to the lab, have them printed (sometimes you must specify NO COLOR CORRECTION or whatever other automatic things labs might do to "enhance" your images) and compare the prints to the softproof. Just like you would do with your printer, but it takes a little longer to get the prints back to your viewing area.
If your display is calibrated and profiled in a way that matches the conditions the labs target values, then the soft proof and the print should match, within the tolerances of your display's capability and your calibration and profiling equipment.
You may want to contact the lab and tell them you want to profile your display according to their suggested target values. Also ask them if they suggest a specific viewing condition - in other words, all of the things you you would typically control in your workflow must now be specified by the lab.
good luck!
kirk