"They neither marry nor are given in marriage" clearly refers to the act of being married. "Marry" and "given" are both verbs(i.e. words used to describe an action, state, or occurrence, and forming the main part of the predicate of a sentence). "To marry" is to perform the act of joining in marriage. "Given" is the past participle of "give", which means freely transfer the possession of (something) to (someone); hand over to. The "they neither marry" would be a reference to men marrying women, and "nor are given in marriage" would be a reference to women being given to men for marriage(according to the custom of that time), cf. Luke 17:27. Let's read the entire account that the given verses are a part of.
Luke 20:27-36 There came to him some Sadducees, those who deny that there is a resurrection, 28 and they asked him a question, saying, “Teacher, Moses wrote for us that if a man's brother dies, having a wife but no children, the man must take the widow and raise up offspring for his brother. 29 Now there were seven brothers. The first took a wife, and died without children. 30 And the second 31 and the third took her, and likewise all seven left no children and died. 32 Afterward the woman also died. 33 In the resurrection, therefore, whose wife will the woman be? For the seven had her as wife.” 34 And Jesus said to them, “The sons of this age marry and are given in marriage, 35 but those who are considered worthy to attain to that age and to the resurrection from the dead neither marry nor are given in marriage, 36 for they cannot die anymore, because they are equal to angels and are sons of God, being sons of the resurrection. (ESV)
The Sadducees, being deniers of the resurrection, plan to trip up Jesus so as to make the resurrection seem like an absurdity. And it's not a terrible plan. The problem is, however, that it lies on an unsubstantiated presupposition; that those who are resurrected will be married..."whose wife will the woman be? for the seven had her as a wife." The Sadducees presupposed that the resurrected children of God are like the "sons of this age" who "marry and are given in marriage". But Jesus corrects this erroneous supposition by answering that the resurrected children of God "neither marry nor are given in marriage". This excludes the "state of being married" for two reasons.
(1) If the resurrected children of God could be married, but could not marry(perform the act of marriage), they would have to be in a state of marriage at the moment of their resurrection, that is to say, they are resurrected IN a state of marriage. But then Jesus' words have no significance. If you are currently IN a state of marriage, it is obvious that you cannot be given in marriage/be joined in marriage. The only ways to do that are to be either polygamous or get divorced(both of which are sinful, the latter under the exception of an act of sexual immorality on the part of either mate[which would also be sinful], and the resurrected children of God are resurrected in perfection, not sinfulness, which makes either option unfeasible). So, if we are resurrected in a state of marriage(and perfection), it is quite evident that we can neither marry nor be given in marriage; there isn't much significance to Jesus' words here.
(2) It doesn't answer the dilemma the Sadducees proffered! If the resurrected children of God are resurrected in the "state of being married", the Sadducees' question remains; to whom is the woman resurrected in a state of marriage? Is it to the first husband? The second? The third, the fourth, the fifth, the sixth, or the seventh? As you can see, the Sadducees' question remains. Jesus' answer would not be an answer!
Jesus' whole point is that the resurrected sons of God do not marry as the sons of this age do, and hence are not married(in a state of marriage). In order to be in a state of marriage, you must, of course, first, get married! Jesus' answer to the Sadducees' dilemma is this; the woman will not be married to any of the men who married her, because she cannot be given in marriage to any of the men who married her! The Sadducees' entire argument lied on an unfounded assumption(e.g. that the woman, after being resurrected, must be married); once Jesus invalidated that assumption by showing the Sadducees that the resurrected sons of God do not marry(and hence are not married[in a state of marriage]), their entire argument was obliterated.
Hope this helps! Have a good day. :)