compensación can mean alimony, so I take it to mean that the costs of the court case will be covered by the one who pays the alimony.

It is a consensual divorce, so it is logical for the parties each to bear their own costs.
Seems to be a 'galicismo' - "compenser les dépenses" is the corresponding phrase in French.

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Note added at 22 hrs (2010-09-24 10:33:11 GMT)
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See Order of the Court of First Instance (now the General COurt) of the EU in Joined Cases Asuntos acumulados T-228/00, T-229/00, T-242/00, T-243/00, T-245/00 a T-248/00, T-250/00, T-252/00, T-256/00 a T-259/00, T-265/00, T-267/00, T-268/00, T-271/00, T-274/00 a T-276/00, T-281/00, T-287/00 y T-296/00. (available on Curia.europa.eu website)

ES: Habida cuenta de la incertidumbre en la que se encontraban inicialmente dichas empresas en lo que atañe a la incidencia de la Decisión impugnada en su situación jurídica y del riesgo de que se les opusiera posteriormente el carácter definitivo de dicha Decisión, no se les puede reprochar que hayan interpuesto los presentes recursos. Por consiguiente, conviene compensar las costas en lo que atañe a dichas empresas demandantes.

EN: In view of the initial uncertainty experienced by those undertakings with regard to the effect of the contested decision on their legal position and the risk that the definitive nature of that decision might subsequently be set up against them, it cannot be held against them that they brought these actions. In relation to those applicants, therefore, the parties must be ordered to bear their own costs.

There is no reason to think that "compensar" in this context bears any different meaning in Peru.

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Note added at 2 days20 hrs (2010-09-26 08:07:24 GMT)
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(Dominican Republic: CÓDIGO DE PROCEDIMIENTO CIVIL,
PROCEDIMIENTO POR ANTE LOS TRIBUNALES)

ARTÍCULO 130. . (Ley 507 de 1941. . Toda parte que sucumba será condenada en las
costas;....

ARTÍCULO 131. . (Ley 296 de 1940. . Sin embargo, se podrán compensar las costas en el todo o en parte entre cónyuges, ascendientes, descendientes, hermanos y hermanas y afines en
los mismos grados. Los jueces pueden también compensar las costas, en el todo o en parte, si los litigantes sucumbieren respectivamente en algunos puntos o cuando concedan un plazo de gracia a algún deudor.

In other words, the unsuccessful party pays the costs. If the parties are both unsuccessful on some heads of claim and successful on others, the parties bear their own costs. It follows that in a consensual divorce the parties would be ordered to pay their own costs.
(I note at this late stage that the document being translated is not from Peru but from the Dominican Republic, hence the above quote).