My family has something like an annual memorial service - once a year, on the anniversary of my mom's death, the priest comes and blesses her grave. He says a short prayer, sprinkles some holy water on the grave, and then leaves. The immediate family (or whomever wants to come) hangs out for a little while (30 minutes tops, usually more like 15-20) and talks about my mom, just generally sharing memories and anything related to her. Then we go out for lunch.
It's a pretty casual thing, so someone's SO would be welcome, but since it's an annual tradition, it's not like any of us need their support like we would at a funeral. It's really an event designed for the immediate family. The SO would probably feel a little awkward as we all hung out around the grave, but overall I would see this particular circumstance as being a non-issue. They could come, or not.
ETA: By immediate family, I mean my sister/brother (my mom's kids) and my grandma and uncle (mom's mom and brother). So this is not a large group of people - usually six or seven people show up a year, depending on circumstances.