Calvin has a maternal grandmother and grandfather. A grandfather who smokes is mentioned, but it is unclear whether he is maternal or paternal. None appear in the strip, and are rarely mentioned.
The grandfather is mentioned during a scene on May 25, 1986, where Calvin smokes a cigarette (and winds up in a coughing fit). Before he does this, Calvin's Mom says: "Sure Calvin. I think your grandfather left some in the back." A reference was made to Calvin's maternal grandfather when Calvin is describing him to Hobbes, echoing Bill Watterson's complaint that comic strips are too small and now look like Xeroxed talking heads (complete with the strip being done with Calvin and Hobbes as motionless "talking heads"). Hobbes then tells Calvin that his grandfather takes comic strips seriously; Calvin says as a result, his mother is looking into nursing homes for him, implying that this grandfather is maternal.
Calvin's maternal grandmother is mentioned after Calvin misbehaved in the doctor's office, when his mother tells Calvin, "Someday I hope you have a kid who puts you through what I have gone through.", to which Calvin replies, "Yeah, Grandma says that's what she used to tell you." She is also mentioned when Calvin's mom is typing on a typewriter. Mom: "Who wrote 'Help I'm a bug' on my letter to Grandma?" (though it's possible she was talking about her own grandmother). In another strip, Calvin is writing a thank-you note to Grandma for sending him a box of crayons as a gift. Hobbes comments on the quickness of the note, and Calvin says "Yeah, I always write her a thank-you note right away...Ever since she sent me that empty box with the sarcastic note saying she was just checking to see if the postal service was still working." Also, in another strip, Calvin makes "funny" expressions on his school pictures and comments that he can't wait for his mom to send his picture to Grandma.