Scalable universal quantum computers require classical control hardware, physically close to the quantum devices at cryogenic temperatures. Such classical controllers need digital memory for various applications, ranging from high-speed queues to high-speed and low-speed lookup tables and working memory. The power consumption of the memories should be within the available cooling power at these temperatures. To obtain the best memory design with the lowest power consumption, cryogenic-CMOS characteristics need to be taken into account during design. This thesis aims to develop a model that can be used to find the optimal memory cell design for each application, while taking area, latency, error rate, and power constraints into account. A model is developed to estimate the error rate and power consumption of a memory core for four cell designs, namely three embedded dynamic cell designs and one static cell design, over a range of applications in terms of memory operation frequency and read/write operation ratio. The model is constructed using room temperature and 233 K simulation data of individual cells and peripherals from a TSMC 40 nm technology. To estimate the error rate and power consumption at 4.2 K, the model is extended with empirical cryogenic-CMOS characteristics, such as an increase in threshold voltage and a steeper subthreshold slope, since good device models at this temperature are not available. To verify and improve the memory model, a test chip in TSMC 40 nm technology is designed, which includes eight fully-custom memories with two threshold-variations of each of the four cell designs to mitigate the cryogenic-CMOS threshold voltage increase. These memories are connected to an on-chip programmable microcontroller through a bus which enables flexible and high-speed testing without the need for high-speed I/O. This chip design is taped out and will be measured to verify and refine the model. At room temperature, the static cell design outperforms the dynamic cells in all memory applications with less than 107 operations per second. However, at cryogenic temperatures, the embedded dynamic cell designs become feasible for applications with more than 300 operations per second, due to the significantly reduced refresh rate. The best embedded dynamic cell design depends on the read/write memory operation ratio required by the application. After verification and improvement of the memory model based on the measurement results from the test chip, this model can be used to find the best cell design for a given application based on its operation frequency and read/write operation ratio. Apart from comparing the performance of a single memory design at room temperature and 4.2 K, this work also allows for direct comparison between the different memory cells designs, designed with the same technology, architecture, peripherals, and by the same design rules. Since only a single architecture is used with a single design for each of the peripherals, further optimisation is required for a cryogenic-optimised full memory design.