If you know that your Grandmother had a still-born birth, you would need to check with your state's (this was in the U.S.?) Dept. of Health - Vital Records Dept. The name of the dept. might vary depending on where this happened.
This is an example, for the state of PA:http://www.portal.state.pa.us/portal/server.pt?open=514&...
If there were any miscarriages, that information would most likely be sealed by confidentiality laws within her medical files. Again, check with the Dept. of Health for particular laws & policies re. access to her information, where these events may have occurred.
Good luck in your research.