Embedding various sensors with powerful computing and storage capabilities in a small communication device, smartphones have become a prominent platform for navigation. With the increasing popularity of Apple CarPlay and Android Auto, smartphones are quickly replacing built-in automotive navigation solutions. On the other hand, smartphones are equipped with low-performance Micro Electro Mechanical Systems (MEMS) sensors to enhance their navigation performance in Global Navigation Satellite System (GNSS)-degraded or -denied environments. Compared with higher-grade inertial navigation systems (INS), MEMS-based INS have a poor navigation performance due to large measurement errors. In this paper, we present laboratory test results on the stochastic and deterministic errors observed in MEMS inertial sensor measurements of five different smartphones from different manufacturers. Then, we describe and discuss the short-term effects of these errors on the pure inertial navigation performance and also on the navigation performance based on the tight coupling of INS with GNSS measurements using a smartphone.