The efficient design of meander line antennas for RFID devices is a significant real-world problem. Traditional manual tuning of antenna designs is becoming impractical for larger problems. Thus the use of automated techniques, in the form of combinatorial search algorithms, is a necessity. Ant colony system (ACS) is a very efficient meta-heuristic that is commonly used to solve path construction problems. Apart from its own native search capacity, ACS can be dramatically improved by combining it with local search strategies. As shown in this paper, applying local search as a form of structure refinement to RFID meander tine antennas delivers effective antenna structures. In particular, we use the operator known as backbite, that has had previous application in the construction of self-avoiding walks and compact polymer chains. Moreover, we apply it in a novel, hierarchical manner that allows for good sampling of the local search space. Its use represents a significant improvement on results obtained previously.