Assess quality of a bandpass filter without human intervention
The Remez exchange algorithm not only returns the optimal filter coefficients but also the approximation error $\delta$. This error determines the maximum amplitude error in the pass bands and in the stop bands. The actual amplitude error in band $i$ is given by $\delta/W_i$, where $W_i$ is the error weight in band $i$.

If the algorithm converges, then you know for sure that the maximum errors $\delta/W_i$ occur at the band edges of band $i$. And you know the band edges because they are part of the specs.