Speech prosody, including pitch contour, word stress, pauses, and vowel lengthening, can aid the detection of the clausal structure of a multi-clause sentence and this, in turn, can help listeners determine the meaning. However, for cochlear implant (CI) users, the reduced acoustic richness of the signal raises the question of whether CI users may have difficulty using sentence prosody to detect syntactic clause boundaries within sentences or whether this ability is rescued by the redundancy of the prosodic features that normally co-occur at clause boundaries. Twenty-two CI users, ranging in age from 19 to 77 years old, recalled three types of sentences: sentences in which the prosodic pattern was appropriate to the location of a clause boundary within the sentence (congruent prosody), sentences with reduced prosodic information, or sentences in which the location of the clause boundary and the prosodic marking of a clause boundary were placed in conflict. The results showed the presence of congruent prosody to be associated with superior sentence recall and a reduced processing effort as indexed by the pupil dilation. The individual differences in a standard test of word recognition (consonant-nucleus-consonant score) were related to the recall accuracy as well as the processing effort. The outcomes are discussed in terms of the redundancy of the prosodic features, which normally accompany a clause boundary and processing effort.