We are interested in model-based testing for real- time systems. Specifically, we study two classes of problems: (I) state identification problems and (II) black-box conformance testing. For state identification problems, we are given the model of a machine with an initial unknown state and we look for an experiment to apply to identify the initial unknown state or the final state to which the machine has moved. For black-box conformance testing, we are given a model of the machine and we want to check whether the machine conforms to its model or not. Before solving state identification problems for timed automata, we study these problems for the case of finite state transducers. For conformance testing, we consider two types of tests: analog-clock and digital-clock tests. We propose a technique for location, edge and state coverage of the specification, by reducing the problem to covering a symbolic reachability graph. We also propose digital- clock test generation techniques based on action refinement. We report on a prototype tool and four case studies: a lighting device, the Bounded Retransmission Protocol, the K9 Mars Rover and the Dala Robot.