The following are excerpts from book II (dealing with Christology) from Robert Bellarmine, Controversies of the Christian Faith (trans. Kenneth Baker; Keep The Faith, 2016).
Bellarmine Presents Calvin’s View that Christ Suffered the Pains of the Damned (Hell)
Calvin in the Institutes, book 2, chapter 16 § 8, 9, 10, 11 and 12, in his small Catechism, in Psychopannychia, in the Harmony of the Gospels on Matt. 27, where he teaches that Christ is said to have descended into the underworld, because he suffered the pains of damned souls . . . Christ, according to Calvin, descended into the underworld because he perceived God as angry with him, and hostile because of us, and that, because of his fear of losing his own salvation he suffered an incredible anxiety of soul, such as one would suffer who knew that he would be lost forever . . . according to Calvin, Christ began to be in hell during the hour in which in the garden he began to be sad and to pray; then he descended, deeper when on the Cross he cried out, My God, my God, etc. . . . Calvin attributes to this infernal suffering almost our whole redemption, so that without this descent into hell, his death on the cross would not be sufficient for our redemption. For he says this in book 2, chapter 16 § 10 in the Institutes: Nothing, he said, would have been accomplished, if Christ had suffered only a bodily death; but at the same time the price of his work was that he should experience the severity of the divine wrath. And after that: Hence also it was necessary that he should struggle with the power of hell and the horror of eternal death, and do it as it were with hands bound together. He repeats the same things, and more at length in his commentary on Matt. 27 . . . . from this flows the incredible blasphemy of this same apostate, which is mentioned by John Cochlaeus in his work on Luther and by Laurentius Surius in his history of the year 1527; the apostate said that Christ despaired and was damned. (pp. 535-36)
You can add to this that the same Calvin in his Commentary on Ps. 22 says that the words, My God, are a correction of what follows, Why have you abandoned me. But who ever heard of a correction being made before the error? Should not the correction follow the error? Therefore, those words did not slip out unwittingly, and then the Lord willingly despaired, if he did despair in any way. Therefore, Calvin has the audacity to add also to his other perverse teachings this one, namely, he attributes to the Lamb of God, who took away the sins of the world, not only sin, but also the greatest sin. (p. 539; emphasis added)
Finally, Christ in the opinion of Calvin, doubted about his salvation, when he descended into the underworld, as we showed above from book 2, chapter 16 § 12 in the Institutes; and the same Calvin in book 3, chapter 2 § 16 in the Institutes teaches that to doubt about one’s salvation is a sin against the virtue of Faith; therefore Christ sinned against Faith. He will respond that the doubt in Christ was not deliberate, but suggested to him by the devil through temptation; for, he responds in this way in the same book 3, chapter 2 § 17 about the faithful, whom he says suffer temptations of doubts concerning the Faith.
But in the same place in § 18 Calvin says that these doubts, although they do not extinguish Faith, still they have their origin in the imperfection of Faith, which, since it does not fully fill us and occupy us, also does not free us from every fault of distrust; therefore he is forced at least to attribute to Christ imperfect Faith and the fault of distrust, since he attributes to him doubts about his own salvation. Behold, therefore, how well Calvin fights for the glory of Christ, when not only does he not attribute to him beatitude with Catholics, but not even perfect faith with the Lutherans. (p. 539)
Bellarmine Refutes Calvin’s View of the Atonement
For it Christ was in hell from the time of his prayer in the garden until the resurrection, and he perceived God as angry and opposed to himself, and if he was not sure about his salvation: why did he say so boldly to Pilate, Hereafter you will see the Son of man coming on the clouds of heaven? (Matt. 26:64). Likewise to Pilate: My kingdom is not of this world? Likewise: Why does he pray to the Father for the men who crucified him? Why did he promise Paradise to the thief? Why did he commend his soul to the Father? Certainly these are not signs of someone doubting the benevolence of the Father, much less of one despairing, or having ear about his own salvation. (p. 537)
[I]f we were redeemed by the hellish sufferings of Christ, signs of this would have had to precede it; also some Sacrament would have to exist in memory of such a benefit, as the Eucharist is in memory of the passion. Likewise, the Church would have to celebrate the memory of such an event, as she celebrates the memory of the birth, passion, death and resurrection of the Lord. Likewise, Christ would have to be depicted in the fire of hell among the damned, as he is wont to he depicted on the cross between two thieves. But we see that none of this has happened, nor so we read that it ever did happen. Therefore, the Church either was always ungrateful, or they are fictions that Calvin teaches. (p. 537)
The fundamental principle of Calvin is false, namely that to be in hell is nothing other than to fear the irate God. For, that is the heresy condemned in Origen, according to Jerome in his letter to Avitus. Moreover, from that principle, it would follow that many people now living are already in hell, and are damned, which conflicts with the certain state of this life. For, how many are found in this life, who have convinced themselves for certain that God is angry with them? How many are there who begin to despair about their eternal salvation? Therefore are all of them now living in hell? What else is this but to deny completely the existence of hell, and to prepare the way for atheism? (pp. 537-38)
Bellarmine Refutes the Penal Substitutionary Reading of Isaiah 53
He takes the first argument from Isa. 53, where Christ is said to be struck by God; for, from this he concludes that God was angry with Christ and hostile to him.
First of all, I respond that Christ is said to be afflicted by the Father, not because the Father hated him, but because he allowed him to be killed for us, as the Apostle explains in Rom. 8:32: He did not spare his own Son but gave him up for us all. Something similar happened, when Abraham wanted to sacrifice his own son, in order to obey God; he did not hate his son, nor did the son think that he hated him, but he understood that it was being done to show obedience to God, without any anger or hated towards himself. Secondly, I say that this affliction is referred by Jerome and by all other Commentators only to the temporal suffering, not to the pains of hell, concerning which none of the ancient authors ever even mentioned, when they reflected on the passion of Christ. Thirdly, I say that it is a fiction invented by Calvin that all who are punished by an irate God are suffering the pains of hell; for, how often does God afflict the impious in this world, but who, because of that, are not said to be already in hell?
The second argument is taken from the same chapter 53 of Isaiah: Upon him was the chastisement that made us whole; therefore Christ had to make atonement for all the punishments which our sins deserved. But our sins deserved not just the death of the body, but also the punishment of hell; Christ, therefore, experienced also the punishment of hell, and so otherwise he would be only the Redeemer of bodies.
I respond: if this argument concluded anything, the Lord should have remained eternally in hell, and suffer an almost infinite number of punishments. For we merited eternal damnation, and we are almost infinite who merited this. Therefore, as Calvin is forced to admit that one temporal punishment of Christ could satisfy for many eternal punishment, so we say that the death of the body of Christ could satisfy for the death of all souls. For, the price of the redemption paid by Christ should not be measured from the multitude, or the quality, or the long duration of his punishments, but from the dignity of the Person who suffered, and from the love with which he suffered. It does not follow that he is the Redeemer only of bodies, both because Christ suffered in mind and in body, but also because one pain of his body had infinite value. (pp. 539-40)