The field of wireless cellular network technology has seen a significant development in recent years, allowing the emergence of many new applications in addition to the traditional mobile phone calls. We are currently implementing the 5G system, which is replacing the previous cellular technologies on the market. Parallel to the development of cellular technologies, wireless local networks based on the IEEE 802.11× standards are rapidly spreading. The desire to use the advantages of both mobile telephony and wireless local networks has led to the idea of integrating the currently used communication systems in one device and requires a well-designed antenna, which should be given a lot of attention when designing the radio system. This article presents the proposed model of a two-band microstrip antenna for which the main assumption is its operating frequencies in the LTE-U (LTE-Unlicensed) band and one of the 5G system bands. The antenna dimensions and parameters have been calculated, simulated, and optimized using CST Microwave Studio software. The developed antenna has a compact structure with dimensions of (60 × 40 × 1.57) mm. The dielectric material RT Duroid 5880 with a dielectric constant εr = 2.2 and thickness h = 1.57 mm was used as a substrate for the antenna construction. The article presents an analysis of the results of simulation and measurements of selected electrical parameters and radiation characteristics of the proposed antenna. The antenna described in the article, working in 5G systems and LTE-U systems, is characterized by two operating bands with center frequencies equal to 3.52 GHz and 5.37 GHz, a low reflection coefficient (for resonances −31.54 dB and −23.16 dB), a gain value of 4.45 dBi, a wide frequency band of 3.0 GHz (68.18%), and a high energy efficiency in the range of 80–96.68%.