Several upper and lower bounds for the numerical radii of 2 × 2 operator matrices are developed which refine and generalize earlier related bounds. In particular, we show that if B, C are bounded linear operators on a complex Hilbert space, then 12max{‖B‖,‖C‖}+14|‖B+C∗‖-‖B-C∗‖|≤w([0BC0])≤12max{‖B‖,‖C‖}+12max{r12(|B||C∗|),r12(|B∗||C|)},where w(.), r(.) and ‖. ‖ are the numerical radius, spectral radius and operator norm of a bounded linear operator, respectively. We also obtain equality conditions for the numerical radius of the operator matrix [0BC0]. As application of the results obtained, we show that if B, C are normal operators then max{‖B+C‖2,‖B-C‖2}≤∥|B|2+|C|2∥+2w(|B||C|).