Dense matrix-matrix operations are relevant for a broad range of numerical applications including those based on machine learning methods. Past research has led to a good understanding of how these operations can be mapped in a generic manner on typical processor architectures with multiple cache levels such that near-optimal performance can be reached. However, while commonly used micro-architectures are typically suitable for such operations, their architectural parameters need to be suitably tuned. The performance of highly optimised implementations of these operations relies on micro-kernels that are often hand-written. Given the increased variety of instruction set architectures and SIMD instruction extensions, this becomes challenging. In this paper, we present and implement a methodology for an exhaustive exploration of a processor core micro-architecture design space based on gem5 simulations. Furthermore, we present a tool for generating efficiently vectorised code leveraging Arm’s SVE and RISC-V’s RVV instructions. It enables automatisation of the generation of micro-kernels and, therefore, the generation of a large range of such kernels. The results provide insights both, to micro-architecture architects as well as micro-kernel developers.