Optical clocks are the most precise frequency measurement devices, with a systematic fractional frequency uncertainty as low as 10−18. While these clocks are typically operated in stationary laboratories, there is a growing interest in implementing transportable optical clocks. As part of this thesis, a transportable 40Ca+/27Al+ quantum logic clock is being developed. For spectroscopy of the 27Al+ clock transition from 1S0 to 3P0, a highly stable UV laser system is required. This thesis focuses on the evaluation of a transportable and highly frequency stable UV laser system built for the 40Ca+/27Al+ clock. The laser system includes a highly frequency stable cavity designed for stabilizing the seed laser frequency and a system for quadrupling the laser frequency without introducing phase disturbances. The cavity consists of a Fabry-P´erot resonator, consisting of a 20 cm long spacer made from ultra-low expansion glass (ULE) with Al0.92Ga0.08As/GaAs mirror coatings on fused silica substrates, optically bonded to the spacer. The calculated thermal noise floor limit is approximately 7-8 × 10−16. The laser is locked to the resonance frequency of the cavity using the Pound Drever- Hall locking technique. A residual amplitude modulation (RAM) stabilization scheme is employed, and the fractional frequency instability limit due to RAM is evaluated. Optical properties such as finesse, linewidth, and birefringence line splitting of the cavity are measured. Additionally, the main sources of relative length change in the cavityare assessed, including vibration noise, photo-thermal noise, and photo-birefringence noise. These noise sources, including RAM, are found to be at or below the thermal noise limit. The cavity is temperature-stabilized using two passive and one active heat shield and is further isolated against temperature fluctuations. The remaining length changes of the cavity due to thermal expansion of the cavity spacer and thermal stress inside the heat shields is evaluated to be dominant over longer timescales. The frequency stability of the cavity is measured by phase comparison with a more stable reference cavity using an optical frequency comb. A fractional frequency instability, represented by the modified Allen deviation, of 2 × 10−16 is achieved. The seed laser frequency is quadrupled using a transportable and compact setup consisting of two single-pass second harmonic generation stages. The single-pass configuration enables phase stabilization of the seed light and UV light throughout the entire setup. The performance of the system is evaluated, demonstrating negligible phase distribution and sufficient UV output power for operating an optical 27Al+ clock. Furthermore, the current status of transportable 40Ca+/27Al+ ion clock is presented, including the physics package with the ion trap in a vacuum chamber, magnets and coils for magnetic field generation, optical paths for ion integration, and the imaging system all mountedon a breadboard.