In this paper the problems of finding error estimates of quadrature formulas are discussed. A method proposed by K.Plukas was tested. One of the most important tests was the one determining the error estimates that are too optimistic. The results have shown that there are 1/8 of such error estimates and that there is no visible pattern when they occur. The second very important test was the one that shows how many iterations are needed to get the estimate of integral. After comparing the results to the ones produced by method of T.O.Espelid it was obvious that method of K.Plukas produced results even when method of T.O.Espelid was not able to. Comparison of these results have also shown that method of K.Plukas is not always as effective as method of T.O.Coteda, i.e. in many cases method of K.Plukas produced the result after more iterations than method of T.O.Coteda.