Error "This user has insufficient permissions to be a portal administrator"

Add the 'Manage Customer Users' Permission on the User's Profile or by Permission Sets
 
In Salesforce Classic 

• If the profile is a custom profile: 

(If 'Enhanced Profile User Interface' is disabled under User Management Settings)

1. Go to Setup | Manage Users.
2. Click Profiles. 
3. Open the profile of the user you wish to be added as portal administrator.
4. Click on Edit.
5. Under General User Permissions, select Manage Customer Users.
6. Click Save.

(If 'Enhanced Profile User Interface' is enabled under User Management Settings)

1. Go to Setup | Manage Users.
2. Click Profiles. 
3. Open the profile of the user you wish to be added as portal administrator.
4. Click on Edit.
5. Under App Permissions, select Manage Customer Users. 
6. Click Save.

• If the profile is a standard profile: 

1. Go to Setup.
2. Click Permission Sets.
3. Click on New. 
4. Name the permission set Manage Customer User or any name you prefer.
5. Enter a description on Description field. 
6. Under App Permissions, select Manage Customer Users.
7. Click Save.
8. Click on Manage Assignments.
9. Click Add Assignments. 
10. Look for the user you wish to add as a portal administrator and the box beside the user's name.
11. Click on Assign.
12. Click Done.

In Lightning Experience

• If the profile is a custom profile: 

(If 'Enhanced Profile User Interface' is disabled under User Management Settings)

1. Go to gear icon | Setup | Users.
2. Click Profiles. 
3. Open the profile of the user you wish to be added as portal administrator.
4. Click on Edit.
5. Under General User Permissions, select Manage Customer Users.
6. Click Save.

(If 'Enhanced Profile User Interface' is enabled under User Management Settings)

1. Go to gear icon | Setup | Users.
2. Click Profiles. 
3. Open the profile of the user you wish to be added as portal administrator.
4. Click on Edit.
5. Under App Permissions,  select Manage Customer Users.
6. Click Save.

• If the profile is a standard profile: 

1. Go to gear icon | Setup | Users | Permission Sets.
2. Click on New. 
3. Name the permission set Manage Customer Users or any name you prefer.
4. Enter a description on Description field. 
5. Under App Permissions, select Manage Customer Users.
6. Click Save.
7. Click on Manage Assignments.
8. Click Add Assignments. 
9. Look for the user you wish to add as a portal administrator and select the box beside the user's name.
10. Click on Assign.
11. Click Done.

Then try adding the user as a portal administrator again. This should not show the error message mentioned anymore. 

Note: There is also a scenario in sandboxes wherein the Manage Customer Users permission will be missing in profiles or permissions sets even if the community feature is enabled in Setup. The issue is that the Community User licenses are not provisioned properly. A quick turnaround is to match the sandbox license from production or refresh from an org where community user license is available for the Manage Customer Users permission to show up in all profiles or permission sets so it can be enabled as discussed above.