SOLUTION (for TezBox web version)
Not as intuitive as one can imagine. The following has been done on a machine with Fedora OS running a Tezos node.
First as a user create a certificate and a key:
openssl req -x509 -newkey rsa:2048 -nodes -keyout server.key -new -out server.crt -subj /CN=localhost -reqexts SAN -extensions SAN -config <(cat /etc/pki/tls/openssl.cnf <(printf '[SAN]\nsubjectAltName=DNS:localhost,DNS:127.0.0.1,IP:127.0.0.1')) -sha256 -days 3650
Install node.js as root:
dnf install nodejs
(the above command will install also npm (js package manager))
install local-web-server, as root:
npm install -g local-web-server
run local-web-server as a user:
ws --https --hostname 127.0.0.1 --key /home/<user>/server.key --cert /home/<user>/server.crt --rewrite '/chains/* ->http://localhost:8732/chains/$1' -v
the command assumes that the certificate and the key are in /home/<user>, the Tezos RPC port is 8732, the default port for 127.0.0.1 is 8000 (the flag -v is for verbose output).
Use Chrome to connect to https://127.0.0.1:8000 and click on proceed to 127.0.0.1 (unsafe)
then type the f12 key and follow "view certificate" -> "details" -> "export" and save the certificate as PKCS #7 Certificates (e.g. output name localhost).
Make sure that nss-tools is installed (for other linux distros it is called libnss3-tools).
From the location where the localhost file has been saved, as a user type:
certutil -d sql:/home/max/.pki/nssdb -A -t "P,," -n localhost -i localhost
Restart Chrome, now connecting to https://127.0.0.1:8000 should not show any warning.
Go to https://wallet.tezbox.com and open an existing/new wallet then go to setting (upper right rod) and replace https://rpc.tezrpc.me with https://127.0.0.1:8000
[addendum 04/10/19] It also works with Opera browser. Instead of using F12 to enter the developers mode, type Ctrl+Shift+I then go to security -> view certificate, the rest is the same. Green light for TezBox connected to a local node using Opera.