Depending upon the length of the relationship and depth, these residues could be scattered and attached/associated to lots of memories. So when you look at the world around you, you would literally see them everywhere, in a lot of things. Its like there is a prom song "You are everything and everything is you" - by stylistics. The title makes no sense to the rational mind at first glance, but it has deep meaning in the metaphorical sense. "You are everything" stands for all the memories and associations(situation, feelings, places, contexts etc) related to that person.
So assuming the relationship ended in a fairly good note or even if it did not assuming you have reached the break even point and are neutral, you could begin to write a reverie which focuses on all POSITIVE memories and associations. It could be in a story form or you could just write down whatever you can brainstorm or remember. Basically, you filter out all the positive associations and memories and re-visualize those before putting them into words. You need to be very objective about this. Like a good memory may be immediately associated by a bad argument that happened after that. But you have to pinpoint your attention to the time when it was good, moment by moment. This strengthens those memories and makes you feel really good overall. By Amplifying those memories you create a much more positive disposition for yourself, improve your mood and the impact of all the negative memories is loosened and reduced. So now when the thought of the person comes, you'll be mostly reminded of points in the reverie and start feeling good. Assuming you remember this person many times in a day, many many times in a week and so on, its a great investment to shift your focus and enjoy each moment you think of them. Reality at all moments is infinite, we can be aware of everything and yet we possess this power of focus. We can focus on whatever gives us maximum reward.
Here's a link that explains a related concept: http://www.yourdailylifecoach.com/disassociation.html