To check port settings an article is there : https://www.apple.com/support/mail-settings-lookup/
Please type your web mail id and its password in the empty field it will give the port numbers , in case if they are incorrect it will show immediately .
And two or three days back I even removed all the SMTP settings and established the server settings with the same method as posted in previous screen shot , it showed no SMTP but it was configured after few minutes .
Also make sure set DNS servers as 8.8.8.8 and 8.8.4.4 , remove any proxies , set location as automatic , wifi security setting as WPA2 personal AES .
Also if you open mail go to connection doctor and it is showing red dot in front of SMTP either it is an issue with port settings or keychains .
Please go to system preferences > internet accounts enter your web mail id & password or if you are using I cloud can you login & also try to login in App Store , I tunes , in www.icloud.com , www.appleid.com if you are unable to login it means keychain is corrupted .
Before following the steps make sure you have four digit I cloud verification code with you in records plus all web mail ids , may be I cloud id , Apple ID and their respective password , even wireless network id & password and registered mobile device .
Click on go to go folder & type ~/Library find keychain folder delete all the contents & empty to the trash , restart & empty the trash , so all passwords are deleted .
NOTE : Be careful do not delete the keychain folder only the contents .
Now again enter system preferences > internet accounts type your web mail & its password , follow upcoming steps and you will enter the web mail .
Open airport utility via spotlight enter your base station password once again .
And for you kind info I am a normal participant here in respectable Apple support community 😎