Delegation question

In my line of work, I delegate a lot of my work to other people and then wait for them to do it. Some respond immediately and say when they’ll get back to me but most others don’t. I usually need to follow up at some point. It creates a low level of background worry that I’ll forget about something. Any advice on how to incorporate delegated work with the planning and scheduling we’re working on this month? And also with the Throw Away your ToDo List?
Thank You.