As others have said, if you stick to pure jQuery your only option is to combine your map with a filter, or otherwise post-process the map results yourself.
However, if you combine jQuery with the popular Underscore.js library, the problem becomes trivial thanks to Underscore's compact method:
var myMap = arr.map(function(e) {
return e.id;
});
myMap = _(myMap).compact();
But if you use Underscore, there's an even simpler way to do the same thing, because Underscore has a method specifically for extracting a certain property from an object:
var myMap = _(arr).pluck('id');
myMap = _(myMap).compact();
You can even chain the two together:
var myMap = _(arr).chain().pluck('id').compact().value();
or you can throw in the Underscore Grease library to get what I consider to be the simplest possible solution:
var myMap = _(arr).pluck_('id').compact();