Hi if6094 (Is it OK to be so informal of me to call you that?
Lora pointed me towards your post. From your description of the cemetery, I suspect you visited the Cathcart Old Parish Church yard (just off Carmunnock Road / Manse Brae).
If you give name and date of the stone you're interested in, I'll have a look, weather permitting. I pass it most weekends but it usually involves climbing a wall to gain entrance.
I've only been to the other Cathcart cemetery (off Clarkston Road) a couple of times and I would not describe it as being in ruins. Cathcart cemetery is vast and is in on two sides of a busy road. Lora, knows it a lot better than me.
If you can check the lair details and which of the cemeteries is involved, we'll try and get it sorted for you.
PS As the mod has changed the title of your thread, you may want to put another post on this board re Hawkhead.