I'm assuming that you are talking about IFR flights inside controlled airspace....
I don't mean to be too flippant (OK , maybe I'm not too bothered) but the answer usually is standard separation. It's a while since I was operational but the rules haven't changed and that's what controllers get paid for. The game is that you have to have at least one form of separation between two aircraft at all times or you lose. At high density units the local procedures may include what are often called deemed separations, procedures that are approved by the relevant aviation authority and although not a full PANS-ATM standard separation, ensure that the aircraft will not get close to each other - for a controller at such a busy airport, deemers are additional rules of the game.
With due respect, to whitelighter, this situation is not an emergency so if the only way to keep the aircraft apart is to use 500ft/emergency separation then either the controller has not managed the situation properly or the procedures are not very robust.
And supraspinatus says 'MA-procedures are often made to keep you safe from terrain'. Now maybe I'm being pedantic but I've never seen a missed approach procedure that is not terrain safe - that's what they are for. It's the controllers job to ensure that he or she has some form of separation between other traffic and the MAP (if it happens) by issuing appropriate clearances.