  In this paper, by constructing some identities, we prove some $q$-analogues
of some congruences. For example, for any odd integer $n>1$, we show that
\begin{gather*} \sum_{k=0}^{n-1} \frac{(q^{-1};q^2)_k}{(q;q)_k} q^k \equiv
(-1)^{(n+1)/2} q^{(n^2-1)/4} - (1+q)[n] \pmod{\Phi_n(q)^2},\\
\sum_{k=0}^{n-1}\frac{(q^3;q^2)_k}{(q;q)_k} q^k \equiv (-1)^{(n+1)/2}
q^{(n^2-9)/4} + \frac{1+q}{q^2}[n]\pmod{\Phi_n(q)^2}, \end{gather*} where the
$q$-Pochhanmmer symbol is defined by $(x;q)_0=1$ and $(x;q)_k =
(1-x)(1-xq)\cdots(1-xq^{k-1})$ for $k\geq1$, the $q$-integer is defined by
$[n]=1+q+\cdots+q^{n-1}$ and $\Phi_n(q)$ is the $n$-th cyclotomic polynomial.
The $q$-congruences above confirm some recent conjectures of Gu and Guo.
