There is no direct equivalent, except in Carbon, which is deprecated.
For detecting the right-click, follow these instructions. They ensure that you will properly detect right-clicks and right-holds and display the menu when you should and not display it when you shouldn't.
For following events, you might try [[NSRunLoop currentRunLoop] runMode:NSEventTrackingRunLoopMode untilDate:[NSDate distantFuture]]
. You will need to call this repeatedly until the user has chosen one of the menu items.
Using nextEventMatchingMask:NSRightMouseUpMask
will not work in all, or even most, cases. If the user right-clicks on your control, the right mouse button will go up immediately after it goes down, without selecting a menu item, and the menu item selection will probably (though not necessarily) happen through the left mouse button. Better to just run the run loop repeatedly until the user either selects something or dismisses the menu.
I don't know how to tell that the user has dismissed the menu without selecting anything.