Each event can be protected with a password. The latest version also allows an invite-per-event thingie (but I think the doc can use a little extra work here).
Btw: don’t use the default event page directly (see the doc: https://www.e-dynamics.be/wordpress/category/documentation/3-installation-and-usage/ )

EME uses that special event page for all kinds of things, so password protecting it is a bit useless.
Best is (like specified in the doc) to use a regular wordpress page and use [eme_events] on it (with all its possible options). That page you can then protect in any way you like.
I will disable the use of the events page itself very soon (so no person can then use that page and get a list of events anymore, because I do understand that bypasses things if you want *all* events to be password protected).
Password protecting an event (or a wordpress page) is a very basic protection (it is only 1 password, easily shared or leaked).
For invites: you don’t need passwords there, just send an event-related mail via EME “send event mail” to your members containing #_INVITEURL and they have the url they can use to book.

The most secure would be to make them wordpress users (so each has his own username/pwd), then link those users to EME users, put those in a EME group and require logged-in people to be a part of that group for RSVP access. Then also the event itself can be marked as “private” so only logged-in persons can see it.