I will first concisely explain the traditional Arminian and Calvinist views, directly addressing (in bold type) the OP's question in the section on Calvinism. I will then introduce one helpful and popular way of comparing the distinctions between traditional Arminian, Calvinist, and Universalist views. At last, I will provide two example alternate views, though there many more.
Calvinism and Arminianism function as internally-consistent rational systems for explaining how God can allow some certain people to become condemned ultimately.
Arminianism remains consistent because it claims that God loves everyone unconditionally, but is unable to save everyone he loves because his character prevents him from infringing upon human will (which assumes that it is not possible to save everyone without infringing upon human will).
Calvinism remains consistent because it claims that God is in fact able to save everyone (regardless of human will), but he has chosen to hate some people in order to demonstrate his glory through wrath and to save other people in order to demonstrate his glory through grace. Thus, he chooses to not save everyone from condemnation. God is not omnibenevolent in the unlimited way in which the OP is using it; God is benevolent to all creatures for some of the time, and some creatures all of the time, but not all creatures all of the time. His wrath as well as his mercy exists to demonstrate his glory.
These are the two most-popular integral Protestant non-Universalist solutions to the dilemma.
Thomas Talbott's Propositions
Thomas Talbott states the above synopses of Arminianism and Calvinism in other words, via his now-famous propositions:
(1) It is God's redemptive purpose for the world (and therefore his will) to reconcile all sinners to himself;
(2) It is within God's power to achieve his redemptive purpose for the world;
(3) Some sinners will never be reconciled to God, and God will therefore either consign them to a place of eternal punishment, from which there will be no hope of escape, or put them out of existence altogether.
If this is indeed an inconsistent set of propositions, as I believe it is, then at least one of the propositions is false. Calvinists reject proposition (1); Arminians reject proposition (2); and universalists reject proposition (3).
(See "The Inescapable Love of God" by Thomas Talbott for more.)
Two Examples of Views Which Are Neither Arminian, Calvinist, nor Universalist
C.S. Lewis' View
It is interesting at this point to note here that C.S. Lewis, in "The Great Divorce", takes something similar in kind to the Arminian view, but changes it sufficiently to make up a rather distinct view. He attempts to show how God never gives up on redeeming souls, so long as there is hope. God provides the means of salvation for perhaps millennia after our deaths, and does not operate his will to condemn anyone ultimately, but, despite his grace, many people will reach a point, by the operation of their own wills, from which God in his foreknowledge knows they will not return. Once that point is reached, in God's wisdom, he will, as it were, "close the gates of Heaven", in order that his grace will not be mocked without end. This results in a view that has aspects of all three primary systems: repentance after death (from Universalism), humans willing themselves into ultimate condemnation (from Arminianism), and God ultimately refusing his grace to certain people (from Calvinism). I find this to be an elegant way to resolve the Biblical and theological difficulties.
Molinism is another attempt to reconcile the difficulties between Scriptural texts which seem apparently Arminian and texts which seem apparently Calvinist. (This view is quite popular among, for example, Baptists.) It centers around the concept of "Middle Knowledge". "Middle Knowledge" is the theoretical knowledge of not only all that has happened, all that is happening, and all that shall happen, but all that could happen and all that could have happened. Molinism asserts that "Middle Knowledge" is indeed possible, and that since it is possible, God of course has it and he takes this knowledge into account in his work of redeeming Creation. The result is that God, before the foundation of the world, peered into all possible timelines and saw the best timeline for maximum salvation (and/or maximum glory, depending upon whether one prefers the Arminian or the Calvinist view of God's goal); he then determined from before time who he would save and who he would condemn, making both a sovereign pronouncement of his grace and an affirmation of humans' use of the power of volition which he willed to grant them.