Puedo devolver el tamaño de pantalla usando:

- (void) getScreenResolution {

    NSArray *screenArray = [NSScreen screens];
    NSScreen *mainScreen = [NSScreen mainScreen];
    unsigned screenCount = [screenArray count];
    unsigned index  = 0;

    for (index; index < screenCount; index++)
    {
      NSScreen *screen = [screenArray objectAtIndex: index];
      NSRect screenRect = [screen visibleFrame];
      NSString *mString = ((mainScreen == screen) ? @"Main" : @"not-main");

      NSLog(@"Screen #%d (%@) Frame: %@", index, mString, NSStringFromRect(screenRect));
    }
}

Salida:

Pantalla # 0 (principal) Marco: {{0, 4}, {1344, 814}}

¿Hay alguna forma de formatear{1344, 814} a1344x814?

Editar:

Esto funciona perfectamente:

- (NSString*) screenResolution {

    NSRect screenRect;
    NSArray *screenArray = [NSScreen screens];
    unsigned screenCount = [screenArray count];
    unsigned index  = 0;

    for (index; index < screenCount; index++)
    {
        NSScreen *screen = [screenArray objectAtIndex: index];
        screenRect = [screen visibleFrame];
    }

    return [NSString stringWithFormat:@"%.1fx%.1f",screenRect.size.width, screenRect.size.height];
}