The TLS protocol is the standard for secure Internet communication between two parties. Unfortunately, there have been recently successful attacks like DROWN or BREACH that indicate the necessity for thoroughly testing TLS implementations. In our research work, we focus on automated test case generation and execution for the TLS security protocol, where the aim is to make use of combinatorial methods for providing test cases that ideally also reveal previously unknown attacks. This is made feasible by creating appropriate input parameter models for different messages that can appear in a TLS message sequence. In this paper, we present the resulting test case generation and execution framework together with the corresponding testing oracle. Furthermore, we discuss first empirical results obtained using different TLS implementations and their releases.