Antenna reconfigurability has attracted great interest in the last years in view of the performance gains it brings about with respect to "static" structures. The benefits are particularly interesting for nowadays compact antennas, as these are subject to conflicting requirements mostly dictated by commercial aspects: increasing device functionality while decreasing volume occupation. This work presents a methodology for the design of compact reconfigurable antennas based on the coupling of engineering expertise with efficient full-wave simulation and automated optimization. The first part provides background material including previous work and description of the relevant computational tools. The second part describes the overall design strategy and demonstrates its application in the solution of challenging design problems of interests for today's applications: frequency/environment reconfigurable operation on a wide operation band. The material presented can be applied in more general optimization tasks in Electromagnetism; therefore it should be of interest to the Antenna/Microwave Engineering practitioner and the Electromagnetic CAE developer.