  Let $A=[A_{ij}]$ be an $n\times n$ operator matrix where each $A_{ij}$ is a
bounded linear operator on a complex Hilbert space $\mathcal{H}$. With other
numerical radius bounds via contraction operators, we show that $w(A) \leq
w(\tilde{A}),$ where $\tilde{A}=[a_{ij}]$ is an $n\times n$ complex matrix with
\begin{eqnarray*} a_{ij}=\begin{cases} w(A_{ii}) \quad \text{if } i=j\\
\underset{0\leq t \leq 1}{\min} \left\| |A_{ij}|^{2t} + |A_{ji}^*|^{2t}
\right\|^{1/2} \left\| |A_{ij}^*|^{2(1-t)}+ |A_{ji}|^{2(1-t)} \right\|^{1/2}
\quad \text{if } i< j 0 \quad \text{if } i> j. \end{cases} \end{eqnarray*} This
bound refines the well known bound $w(A) \leq w(\hat{A}),$ where
$\hat{A}=[\hat{a}_{ij}]$ is an $n\times n$ matrix with $\hat{a}_{ij}= w(A_{ii})
$ \text{if } $i=j$ and $\hat{a}_{ij}= \|A_{ij}\| $ \text{if } $i\neq j$ [Linear
Algebra Appl. 468 (2015), 18--26]. We deduce that if $A$, $B$ are bounded
linear operators on $\mathcal{H},$ then \begin{eqnarray*}
w\left(\begin{bmatrix} 0&A\\ B&0 \end{bmatrix}\right) \leq \frac12 \left\|
|A|^{2t} + |B^*|^{2t} \right\|^{1/2} \left\| |A^*|^{2(1-t)}+ |B|^{2(1-t)}
\right\|^{1/2} \quad \text{for all } t\in [0,1]. \end{eqnarray*} Further by
applying the numerical radius bounds of operator matrices, we deduce some
numerical radius bounds for a single operator, the product of two operators,
the commutator of operators. We show that if $A$ is a bounded linear operator
on $\mathcal{H},$ then $w(A) \leq \frac12 \|A\|^t \left\| |A|^{1-t}+|A^*|^{1-t}
\right\| \quad \text{for all } t\in [0,1],$ which refines as well as
generalizes the existing ones.
