Do this:
Open the email where the institution asked you for the passport.
Right click and select "Show headers" or something similiar.
Then check the topmost "Received:"-header, and walk downwards. Disregard any headers with 127.*.*.*
IP, a 192.168.*.*
IP, or a adress between 172.16.*.*
to 172.31.*.*
(as these usually is internal communication between spam filters, antivirus engines and other mail-handling software local to your provider).
When you have arrived at the first public header, read if encryption was used.
Example of encrypted mail:
Received: from THE_REPUTABLE_INSTITUTION (THE_REPUTABLE_INSTITUTION [THEIR_IP])
(using TLSv1.2 with cipher ECDHE-RSA-AES256-SHA (256/256 bits))
(No client certificate requested)
by YOUR_EMAIL_PROVIDER (Postfix) with ESMTPS id C98D076010F
for <YOUR_EMAIL>; Wed, 20 Sep 2017 09:10:45 +0200 (CEST)
Example of a nonencrypted mail:
Received: from THE_REPUTABLE_INSTITUTION (THE_REPUTABLE_INSTITUTION [THEIR_IP])
by YOUR_EMAIL_PROVIDER (Postfix) with SMTP id 1359D7600C2
for <YOUR_EMAIL>; Sat, 16 Sep 2017 21:03:38 +0200 (CEST)
Now when you have verified the email is encrypted in-transit, just send the passport. (Actually, I had a hard time finding a non-encrypted email in my mailbox with over 200+ emails, thats how common email encryption has become today)
This isn't a 100% foolproof method, as the mail might be encrypted one-way only, eg your mail provider does receive but not send encrypted mail, or the institution does send encrypted mail but not receive one.
But it should be sufficent for your purposes.
If you haven't received a mail from them, just send a email. As a bonus, ask them to "forward your original email as attachment to you", then you can even see if they received the email encrypted.
Note that this method can only be used for non-regulated communication, eg where you isn't REQUIRED to secure the communication, but you WANT. If there is regulations for securing the communication, for example PCI-DSS or HIPAA or similiar, then email is usually specifically prohibited, regardless of its encrypted or not, and then you can read in the regulations how the information should be transferred. Usually over registred snail-mail unless urgent, then faxing is allowed.