Requirements Satisfaction Assessment (RSA) evaluates whether the set of design elements linked to a single requirement provide sufficient coverage of that requirement -- typically meaning that all concepts in the requirement are addressed by at least one of the design elements. RSA is an important software engineering activity for systems with any form of hierarchical decomposition -- especially safety or mission critical ones. In previous studies, researchers used basic Information Retrieval (IR) models to decompose requirements and design elements into chunks, and then evaluated the extent to which chunks of design elements covered all chunks in the requirement. However, results had low accuracy because many critical concepts that extend across the entirety of the sentence were not well represented when the sentence was parsed into independent chunks. In this paper we leverage recent advances in natural language processing to deliver significantly more accurate results. We propose two major architectures: Satisfaction BERT (Sat-BERT), and Dual-Satisfaction BERT (DSat-BERT), along with their multitask learning variants to improve satisfaction assessments. We perform RSA on five different datasets and compare results from our variants against the chunk-based legacy approach. All BERT-based models significantly outperformed the legacy baseline, and Sat-BERT delivered the best results returning an average improvement of 124.75% in Mean Average Precision.