The death of a grandparent can bring with it an assortment of emotions. If the girl you love has the unfortunately unavoidable misfortune of losing her grandmother, being there to support her and cheer her up is a kind thing to do. While you certainly won't be able to take away all of the sting associated with this loss, kindness and consideration on your part may help her come to terms with the loss and get back to her cheery self a bit more rapidly.
Listen to her vent. When going through the grief process, sharing your pain can be cathartic. Allow your girlfriend to benefit from letting out her emotions by being willing to sit and listen to her talk. Don't push her to speak about her grandmother, but if she wants to, be there to support her, acting as the shoulder upon which she can cry.
Surprise her with a thoughtful gift. Showing your girlfriend that you support her is a wonderful way to help her feel less alone in her grief. Get your girlfriend a surprise bouquet of flowers for no reason other than to show her that you care. Or go the extra mile and get her something related to her grandmother, such as a locket featuring a picture of this beloved relative.
Take her away. Sometimes, getting away from it all is the best way to move on from the heartbreak associated with death. After the dust has settled and the memorial and funeral are over, plan a weekend away for your girlfriend. Take her to a secluded cabin or a nearby coastal area and spend the weekend having fun, relaxing, and letting go of all worries.
Be patient. Despite how much you hate to see your girlfriend down in the dumps, when you lose someone, time is the only thing that will really heal the wound. Don't feel like you are a failure as a boyfriend if your romantic attention doesn't immediately brighten her disposition. Instead, be supportive for as long as she needs, giving her time to go through the grief process.