Performing conventional mechanical characterization techniques on soft materials can be challenging due to issues such as limited sample volumes and clamping difficulties. Deep indentation and puncture is a promising alternative as it is an information-rich measurement with the potential to be performed in a high-throughput manner. Despite its promise, the method lacks standardized protocols, and open questions remain about its possible limitations. Addressing these shortcomings is vital to ensure consistent methodology, measurements, and interpretation across samples and labs. To fill this gap, we examine the role of finite sample dimensions (and by extension, volume) on measured forces to determine the sample geometry needed to perform and unambiguously interpret puncture tests. Through measurements of puncture on a well-characterized elastomer using systematically varied sample dimensions, we show that the apparent mechanical response of a material is in fact sensitive to near-wall effects, and that additional properties, such as the sliding friction coefficient, can only be extracted in the larger dimension case where such effects are negligible.