Badly, like most people who have a good relationship with their parents I imagine. My mother died in 2009 and my father in 2014. The first one was rough, she was unexpectedly diagnosed with stage 4 cancer and only lasted a few months after that. The second one was fucking brutal though, I was the one who had to make the call to pull him off of life support (he had a DNR from pretty much the moment mom died), on the phone, from ~1500 miles away.
They hit me very different, for pretty obvious reasons, but also some not-obvious ones. Plus that was further complicated by the fact that despite loving my parents very much (they were flawed like everyone else, but honestly they were the best parents a guy could ask for) I never cried at either of their deaths. I didn't get to attend the service for either one (not that there was much of one). But it would hit me out of the blue for years. I still dream about them sometimes. But it wasn't until my best friend of ~25 years (and long-time roommate) died in 2019 (it was a rough 10 years) that it really all hit me, I felt utterly alone and rudderless in the world for a good while afterwards.
I'm doing better now thankfully. You have no choice but to keep on keeping on, but now carrying that weight. It doesn't ever go away, but it does get lighter with time.