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The goal of the Dagstuhl Seminar 19301 ``Secure Composition for Hardware System'' was to establish a common understanding of principles and techniques that can facilitate composition and integration of hardware systems to achieve specified security guarantees. Theoretical foundations of secure composition have been laid out in the past, but they are limited to software systems. New and unique security challenges arise when a real system composed of a range of hardware components, including application-specific blocks, programmable microcontrollers, and reconfigurable fabrics, are put together. For example, these components may have different owners, different trust assumptions and may not even have a common language to describe their security properties to each other. Physical and side-channel attacks that take advantage of various physical properties to undermine a system's security objectives add another level of complexity to the secure composition problem. Moreover, practical hardware systems include software of tremendous size and complexity, and hardware-software interaction can create new security challenges. The seminar considered secure composition both from a pure hardware perspective, where multiple hardware blocks are composed in, e.g., a system on chip (SoC), and from a hardware-software perspective where hardware is integrated within a system that includes software. The seminar brought together researchers and industry practitioners from fields that have to deal with secure composition: Secure hardware architectures, hardware-oriented security, applied cryptography, test and verification of security properties. By involving industrial participants, we were able to get insights on real-world challenges, heuristics, and methodologies employed to address them and initiate a discussion towards new solutions.