In adition to crisvdb answer, I've several information to add and is the continuation of the walktrough. I don't comment because is pretty complex comment this, but before this answer take a look to crisvdb answer first and then return to continue.

1. You can make your cert in any folder, can be or can't be in the same folder of the app.
2. Take openssl verify -CAfile localhost.crt localhost.crt as not optional step, mandatory. It will help.
3. Do not recompile or touch the code meanwhile you are doing this, in order to get first scenario clean.
4. In some distributions, as Raspbian for Raspberry Pi, CA certificates are located in /etc/ssl/certs as well as /usr/share/ca-certificates/ and in some cases /usr/local/share/certificates.
5. Do not copy the cert manually to trusted certs, run sudo update-ca-certificates
6. If you use a password while making the certificate, you should use it in the appsettings.json
7. If you get this error:

Interop+Crypto+OpenSslCryptographicException: error:2006D002:BIO routines:BIO_new_file:system lib

Take in consideration that error means "access denied". It can be because you don't have permissions or related.

7b) Could be also that the file is not found, I use the entire path in the config:

 "Path": "/home/user/www/myfolder1/myapp/localhost.pfx",

8. After that, and if everything works, you could see a 500 error if you are using Apache or Apache2.

If you get the following error in the apache logs of the site:

[ssl:error] [remote ::1:yourport] AH01961: SSL Proxy requested for yoursite.com:443 but not enabled [Hint: SSLProxyEngine] [proxy:error] AH00961: HTTPS: failed to enable ssl support for [::1]:yourport (localhost)

you must set in the VirtualHost the following configuration after SSLEngine On and before your ProxyPass

SSLProxyEngine on

9. After that, and if everything works, you could see a 500 error if you are using Apache or Apache2.

If you get the following error in the apache logs of the site:

[proxy:error] [client x.x.x.x:port] AH00898: Error during SSL Handshake with remote server returned by / [proxy_http:error] [client x.x.x.x:port] AH01097: pass request body failed to [::1]:port (localhost) from x.x.x.x()

you must set in the VirtualHost the following configuration after SSLProxyEngine on and before your ProxyPass

SSLProxyVerify none
SSLProxyCheckPeerCN off
SSLProxyCheckPeerName off

UPDATE

If you are renovating this, and using the same names, take in consideration that you should remove your pem file from etc/ssl/certs

While the answer provided by @chrsvdb is helpful it does not solve all problems. I still had issue with service-to-service communication (HttpClient - PartialChain error) and also you must reconfigure Kestrel to use your own certificate. It is possible to create a self-signed certificate and import it to the .NET SDK. All you need is to specify the 1.3.6.1.4.1.311.84.1.1 extension in the certificate.

After that the cert can be imported into .NET Core SDK and trusted. Trusting in Linux is a bit hard as each application can have it's own certificate store. E.g. Chromium and Edge use nssdb which can be configured with certutil as described John Duffy. Unfortunately the location to the nssdb maybe different when you install application as snap. Then each application has its own database. E.g. for Chromium Snap the path will be $HOME/snap/chromium/current/.pki/nssdb, for Postman Snap the will be $HOME/snap/postman/current/.pki/nssdb and so on.

Therefor I have created a script which generates the cert, trusts it for Postman Snap, Chmromium Snap, current user nssdb and on system level. It also imports the script into the .NET SDK so it will be used by ASP.NET Core without changing the configuration. You can find more informations about the script in my blog post https://blog.wille-zone.de/post/aspnetcore-devcert-for-ubuntu

Looks like this is a known issue with dotnet global tools and that specific command is only available for MacOS and Windows. See this issue on github: Issue 6066.

It seems like there may be a work around for Linux users based on this SO post: ASP.Net Core application service only listening to Port 5000 on Ubuntu.

For Chrome:

1. Click "Not Secure" in address bar.
2. Click Certificate.
3. Click Details.
4. Click Export.

Run: certutil -d sql:$HOME/.pki/nssdb -A -t "P,," -n {FILE_NAME} -i {FILE_NAME}

Restart Chrome.