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Lightweight cryptography offers viable security solutions for resource constrained Internet of Things (IoT) devices. However, IoT devices have implementation vulnerabilities such as side channel attacks (SCA), where observation of physical phenomena associated with device operations can reveal sensitive internal contents. The U.S. National Institute of Standards and Technology has called for lightweight cryptographic solutions to process authenticated encryption with associated data (AEAD), and is evaluating candidates for suitability in a Lightweight Cryptography (LWC) Standardization Process. Two Round 2 candidate variants, COMET-CHAM and SCHWAEMM, use Addition-Rotation-XOR (ARX) primitives. However, ARX ciphers are known to be costly to protect against certain SCA. In this work we implement side channel protected versions of COMET-CHAM and SCHWAEMM using register transfer level design. Identical protection schemes consisting of a threshold implementation (TI)-protected Kogge-Stone adder are adopted. Resistance to power side channel analysis is verified on an Artix-7 FPGA target device. Implementations comply with the Hardware API for Lightweight Cryptography, and use a custom-designed extension of the Development Package for the Hardware API for Lightweight Cryptography which enables test and evaluation of side channel resistant designs. We compare side channel protection costs of the two candidates against each other, against their unprotected counterparts, and against previous side channel protected AEAD implementations. COMET-CHAM is shown to consume less area and power, while SCHWAEMM has higher throughput and throughput to area ratio, and is more energy efficient. On average, the costs of protecting these ciphers against SCA are 32% more in area and 38% more in power, compared to the average protection costs for a large selection of previously-evaluated ciphers of similar implementation. Our results highlight the costs involved in implementing side channel protected ARX-ciphers, and help to inform NIST LWC late round and final portfolio selections.