Unless you are both using some pre-agreed encryption utility like PGP, then the other person needs to be using the same service as you.
From there, it depends how much guarantee you are looking for. There are some for general security, and then there are the ones that someone like Austin Powers would need, as in the company is incapable of handing over encryption keys to some government who demands them.
For everyday security, I've been hearing a lot about Protonmail. It's not going to keep you safe from powerful forces who are trying to observe you.
If you have something that needs a critical level of privacy, I always feel it is safer to agree with the other person to use your own highly rated encryption tool instead of depending on some website to do it for you.
What are we up to. 512, 1028-bit encryption these days? The higher the better. Those quantum computers aren't very far away from deciphering things that used to be though secure, so keep that future in mind.