Suppose [Aij] is an n×n operator matrix, where each Aij is a bounded linear operator on a complex Hilbert space H. Among other inequalities, it is shown that w([Aij])≤w([aij]), where [aij] is an n×n matrix with (Formula presented.) This numerical radius bound refines a well known bound by Abu-Omar and Kittaneh [Linear Algebra Appl. 468 (2015), 18–26]. We use these estimates to derive several numerical radius inequalities and equalities for 2×2 operator matrices. Applying these inequalities, we also deduce several numerical radius bounds for a bounded linear operator, the product of two operators and the commutator of operators. In particular, it is shown that (Formula presented.) where A is a bounded linear operator on H. This bound refines as well as generalizes the well known bounds.