For the sake of both the environment and human health, it is necessary to reduce meat consumption. However, increased consumer adoption of plant-based meat alternatives (PBMAs) will only occur when such products are attractive. PBMAs with meat-like sensory attributes and those that can be cooked similarly to meat are known to be preferred, but the preference for meat-likeness varies depending on the consumer’s attitude towards meat. This study determined the relationship between consumers’ level of meat attachment (MA) on their sensory perceptions of and preference for commercial PBMAs, and their drivers of liking. MA was measured by the Meat Attachment Questionnaire (MAQ); consumers with either low or high MA (LMA and HMA, respectively) were invited to participate in the study (n = 99). The sensory characteristics of seven PBMAs were evaluated using a rate-all-that-apply (RATA) questionnaire, along with an ideal profile and product hedonics. Consumers with LMA had significantly higher overall, aroma, and taste liking, compared with consumers with HMA. Both LMA and HMA consumers similarly discriminated among the sensory properties of PBMAs and the ideal profile. Nevertheless, a further adapted penalty analysis showed subtle differences in consumers’ penalisation of sensory attributes depending on MA level. These findings could be used for future research and the development of PBMAs based on consumers’ MA; they could also be extended for application in a meal context where the PBMAs are consumed.