Joel Garver, ubiquitous in his learning and lauded by divines across the world, has translated a letter from John Davenant to Samuel Ward, and he has also reposted a letter from Ward to Archbishop Ussher. Both letters have to do with the efficacy of infant baptism.
Davenant’s letter to Ward is here.
Ward’s letter to Ussher is here.
Both men affirm that some type of grace is given to all in baptism. Particularly, they affirm that original guilt is taken away from all baptized infants.
Davenant also affirms some critical distinctions between “efficacy” in infants and “efficacy” in those who have reached the age of reason. Two particularly important statements that he makes are:
That the justification, regeneration, adoption, which we admit does belong to baptized infants, is not univocally the same with that justification, regeneration, and adoption, which we say is never lost with regard to the matter of the saints’ perseverance.
and:
The justification and regeneration and adoption of baptized infants confers on them a state of salvation according to the condition of infants.
So baptized infants have “infant benefits” so to speak. These are not the same as those possessing full use of their reason, which would be the ever-persevering benefits. However, these “infant benefits” are sufficient for the infants’ salvation prior to reaching such age.
I believe this is essentially Calvin’s position as well, and it is how we should understand his own language of people rejecting the grace that was given to them at baptism. Compare what we’ve seen in Davenant to this from Calvin:
It is certainly true that when children of believers reach the age of discernment [and have never repented or believed] they will have alienated themselves from God and destroyed utterly the truth of baptism. But this is not to say that our Lord has not elected them and separated them from others in order to grant them His salvation. Otherwise, it would be in vain for Saint Paul to say that a child of a believing father or mother is sanctified, who would be impure if he were born of and descended from unbelievers (1 Cor. 7:14).
~ John Calvin, Treatises Against the Anabaptists and Against the Libertines pg. 52
Wedgewords 
Btw, Anthony Burgess has some good criticisms of Ward and Davenant on this issue. Also Gataker, another Westminster Divine, debated Ward.
Witsius (in his Miscellanies, I believe), Baxter, and Mastricht also criticize the position of Davenant and Ward (a position also shared by Forbes, Hooker, Jurieu, etc.).
While I’ve read Gataker, Burgess, Baxter, and Mastricht on this, I didn’t find them entirely convincing, especially in the face of the seemingly more catholic witness of Davenant, et al – though personally I wouldn’t be overly dogmatic on the issues involved, qualifying any opinion as only “probable.”
Davenant’s position is also articulated by Cornelius Burges, who gives a list of other divines who hold it.
According to Burges, these divines include: Calvin, Peter Martyr, Zanchius, Musculus, Junius, Marloratus, Bucer, Pareus, Daneus, Chamier, Vobius, Jewel, Whitaker Fulke, Davenant, White, Featly, Ames, Richard Hooker, Thomas Rogers, Thomas Taylor, and Aynsworth.