Living wage (LW) is a concept that goes beyond that of national minimum wage (NMW), since it implies income adequacy to the wage earners and to his/her family members. It is coherent with the principle related to wages of the European Pillar of Social Rights (EPSR) namely the right of workers to fair wages, and the duty to ensure adequate minimum wages providing the satisfaction of the worker needs and of his/her family, which originated a proposal of the European Commission for a Directive on adequate minimum wages in the European Union. This article discusses the possibility of implementation of a LW policy in Portugal, a country with low average and median wages, a generous NMW relative to average and median wage, high earnings inequality and a polarised labour market. To be defensible, this policy should reach household income adequacy, be feasible regarding the labour and fiscal costs, and be socially acceptable regarding the change of earnings distribution. The discussion of this policy is made using EU-SILC data and data from interviews with social partners involved in the national level social dialogue. We quantify and qualify some of the trade-offs, simulating different values for core policy variables, centred on the worker as a wage earner, as a household member and as a citizen with social rights and fiscal duties, supported on an adequate normative estimation of a consensual Minimum Income Standard (MIS) for the Portuguese households.