Solution:

Let the numbers be $a,b,c,d$ in order.

Since the average of $a$ and $b$ is $21,$ we know their sum is $21\cdot2 = 42.$
Since the average of $c$ and $d$ is $30,$ we know their sum is $30\cdot2 = 60.$
Since $a+b = 42$ and $c+d = 60 ,$ we know $$\begin{align*} a+b+c+d &= 42 + 60\\ &= 102 \end{align*}$$

Now, with the average of $b$ and $c$ being $26,$ we know their sum is $26\cdot2=52.$ This means $b+c = 52.$

Subtracting this result from the sum of all the terms yields $a+d =50.$
Since $\dfrac{a+d}{2}=25,$ our answer is $25.$

Thus, the correct answer is B.