Take out in the old port
Are you staying at the Delta on University? That's in what they call the International District. It's close to downtown and Old Montreal, but a bit far from the Old Port. There's not much take out there. Most non-fancy places are open for lunch and often only weekdays. I worked around there a few years ago and decent delivery options were few and far between on weekdays and non-existent on weekends. I don't know if things have changed much.
You could always use À La Carte Express although it's not very good value, or ask your concierge for some take-out menus.
Ditto what SnackHappy said about your actual neighbourhood - Delta University is not the Old Port, but is close to Old Montreal and down the hill from downtown. Here's a thread that might help:
Restaurant delivery suggestions for Montreal (Old Montreal)?
A la carte is pretty bad value...
A few places that will deliver (though none are fantastic) are Boustan (lebanese pitas and whatnot) , Il focolaio really good pizza, alto for anything (their poutine and fries suck), sandhu for anything, pitarifique for pitas, wok cafe for chinese.