Let U0 denotes intercept variance and U1 denotes slope variance.

Given that the coverage rate for the intercept variance is 91% (U0) , and the coverage rate for the slope variance is 91.2% (U1) . Also nominal coverage rate is 95%.

Then it is written that

I have not understood from the information of "coverage rate for the intercept variance 91% (U0) and coverage rate for the slope variance 91.2% (U1)", how is the calculation "the standard errors for the variance components are estimated about 15% too small" derived ?

For double check , you can consider the following :

The coverage rate for slope variance is 91.2%. This amount implies that the standard errors for the slope variance is estimated about 3.1% too small when the nominal coverage rate is 95%.

Any help is appreciated. Thanks in advance.

Given that the coverage rate for the intercept variance is 91% (U0) , and the coverage rate for the slope variance is 91.2% (U1) . Also nominal coverage rate is 95%.

Then it is written that

The amount of coverage here implies that the standard errors for the variance components are estimated about 15% too small.

For double check , you can consider the following :

The coverage rate for slope variance is 91.2%. This amount implies that the standard errors for the slope variance is estimated about 3.1% too small when the nominal coverage rate is 95%.

Any help is appreciated. Thanks in advance.

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