How to add a .crt certificate to iPhone's keychain?
Updated for iOS 12.0.1
As Andrew and Michal mentioned, apparently iOS only allows the Mail and Safari apps to open and install certificates. Other apps are blocked from opening certificates.
So here is how I got mine working:

Put my certificate file (mycertificate.crt) on my private local server temporarily.
Using iOS Safari (very important), browse to my https://mylocalsite.test/mycertificate.crt
You'll probably see a &quot;This Connection Is Not Private&quot; warning and need to click &quot;Show Details&quot; &gt; &quot;visit this website&quot;.
When prompted with &quot;This website is trying to open Settings to show you a configuration profile. Do you want to allow this? [Ignore or Allow?]&quot;, choose &quot;Allow&quot;.
You'll now be in your iPhone Settings &gt; Install Profile. Click &quot;Install&quot; to install the certificate.
Enter your passcode to confirm.
You'll see a warning telling you &quot;This certificate will not be trusted for websites until you enable it in Certificate Trust Settings.&quot; Press &quot;Install&quot; to proceed.
Press &quot;Done&quot;.
Visit Settings &gt; General &gt; About &gt; Certificate Trust Settings
&quot;Enable full trust for root certificates&quot; for the newly-installed certificate.
(Restarting the phone does not seem to be necessary.) I was immediately able to use Chrome to browse to my site using https, and it worked as I hoped.

These other links helped me, too:

https://support.apple.com/en-us/HT204477
https://support.securly.com/hc/en-us/articles/206978437-How-to-deploy-Securly-SSL-certificate-to-iOS-
For generating a local Certificate Authority and self-signed certificate, my favorite approach as of 2020-09-14 is https://github.com/FiloSottile/mkcert