The Bishop of Porto Cathedral's official residence is called the Paço Episcopal. The symmetric boxy exterior dramatically contrasts with the Romanesque style of the Cathedral. They compliment each other. It is not open to the public.
Porto's Bishops Residence is next to the Cathedral on the south side of the square
If you stand with your back to the entrance to the cathedral, facing the square, look to your left. That white building with the ornate highly decorative late baroque and rococo style stonework around each window and door is the Bishops Residence, the Episcopal Palace. It was built in the later part of the 1100s and rebuilt in the 1700s in the form you see today by architect Nicolau Nasoni.
A bishop in the Roman Catholic Church is responsible for governing and teaching doctrine to the Catholics within his jurisdiction. Most cathedrals are overseen by a Bishop who leads services with the assistance of other lower ranked priests. In the past they have acted as judges in ecclesiastical courts. They still preside over disagreements within the church.
They have a dioceses attached to their cathedral to oversee. This means they are responsible for the good running of the churches and parishes in a particular area of the country. The Catholic Church believes that the origins of the office of bishop goes back to the apostles. The Church believes they were endowed with a special charism by the Holy Spirit at Pentecost. Catholics believe that by the laying on of hand in the sacrament of holy Orders this gift is transmitted through an unbroken succession of Bishops to do God's work.
The Bishop of Porto's Palace is next to the Cathedral of Porto