Simultaneous interpretation is an especially challenging form of translation because it requires converting speech from one language to another in real-time. Though prior work has relied on out-of-the-box machine translation metrics to evaluate interpretation data, we hypothesize that strategies common in high-quality human interpretations, such as summarization, may not be handled well by standard machine translation metrics. In this work, we examine both qualitatively and quantitatively four potential barriers to evaluation of interpretation: disfluency, summarization, paraphrasing, and segmentation. Our experiments reveal that, while some machine translation metrics correlate fairly well with human judgments of interpretation quality, much work is still needed to account for strategies of interpretation during evaluation. As a first step to address this, we develop a fine-tuned model for interpretation evaluation, and achieve better correlation with human judgments than the state-of-the-art machine translation metrics.