Integrated circuits such as programmable logic device integrated circuits with memory interface circuitry are provided. The memory interface circuitry measures the timing characteristics of an associated memory during a series of dummy read operations. A multiplexer and phase detector are used to measure phase shifts of memory group clock signals compared to a system clock signal. The memory interface circuitry uses these measurements to adjust a delay-locked-loop circuit. The delay-locked-loop circuit produces a capture clock that is used to read data from the memory.