This paper explores the generation of conformance test cases for Recursive Tile Systems (RTSs) in the framework of the classical ioco testing theory. The RTS model allows the description of reactive systems with recursion, and is very similar to other models like Pushdown Automata, Hyperedge Replacement Grammars or Recursive State Machines. Test generation for this kind of infinite state labelled transition systems is seldom explored in the literature. The first part presents an off-line test generation algorithm for Weighted RTSs, a determinizable sub-class of RTSs, and the second one, an on-line test generation algorithm for the full RTS model. Both algorithms use test purposes to guide test selection through targeted behaviours. Additionally, essential properties relating verdicts produced by generated test cases with both the soundness with respect to the specification, and the precision with respect to a test purpose, are proved.