[exim] TLS Base64 unexpected header error

I'm getting this error. I recently migrated from one server to another,
and since then I am seeing this in my logs:

TLS error on connection from xxxx(cert/key setup:
cert=/etc/ssl/certs/mail_seiner_com.pem
key=/etc/ssl/localkeys/mail.seiner.com/mail.seiner.com.key): Base64
unexpected header error.

I am running Exim4.82.

I am using the same certs as I did on my other server. Unfortunately the
older server is not accessible at the moment and may not be for weeks.

I've been through much of the google-suggested remedies and nothing has
helped. The certs are downloaded from Comodo and visually look fine -
no extra characters, no extra whitespace.

What should I be looking at/for?

Thanks.