The initiator of the conversation that it would be better to stay friends, can act as male or female is not important. Who of the lovers has great diplomatic abilities, and more eloquent, as they say, and the cards. During a conversation in every way refrain from accusations, charges, claims, even in the most discrete, tactful manner. On the contrary, nobly take the blame for the resulting cooling itself. Pay tribute to your partner, tell that you were very good with him that you will forever keep in my memories.
Certainly reassure that you'll be ready at any moment to help, to provide support. Of course, asking nothing in return.
Suppose, in coordination with the partner you took a kind of timeout, i.e. some time stopped close relationship to once again get a head count to decide. Then act reasonably and with restraint. You should not tell your relatives, friends, co-workers about your cooling, especially, to complain, to accuse the other side of the gap, say nasty things. Remember that word travels fast, and these data will soon become accessible to your ex half. Will it be possible then to maintain friendly relations – the question is purely rhetorical.
If after the timeout the breakup happened, try at least two to three weeks to remind myself. After all, your partner should simply calm down, to get rid of emotions, get used to the idea that the affair really ended. And then call or under the pretext try to meet, ask for business, ask if they need your help or advice.
With such tactics, your relationship can remain friendly. And who knows, maybe with time you will understand that you made a mistake and want to start your romance again.