In Brazil, the rulers of some cities already apply the payment for environmental services. Especially if it is of interest to the government as producing areas of water. The law still is processing some changes in the law. Let's wait.
Payment for ecosystem services is one of the essential approach for Sustainable Forest Management. It is picking momentum in the management of many protected areas in this part of the world. However, there is shortage of scientific studies and publication on these aspects.
The known cases of payments for ecosystem services in grasslands are in Central America. In mexico there are pine forests slopes around the state of mexico that supply drinking water to the federal district. There are cases in Brazil in upper parts of the basins and the system call mine water. See in spanish Stefano pagiola et al 2004 Pago por Servicios de Conservación de la Biodiversidad en Paisajes Agropecuarios.
Many Protected Area (PA) management/ ecotourism projects in the forestry sector in different states in India are modeled for payment of ecosystem services. However, we are yet to declare it as successful as it requires close monitoring & course corrections to meet their different objectives.
I'm not aware of any PES programs that specifically target grasslands. The vast majority focus on forests, and most of the others (that I know of) on agricultural areas. But the issues are likely to be similar. Are there particular features of a grassland ecosystem (or, perhaps, of the specific grassland ecosystem that interests you) that might make you think that PES would work differently there than in a forest? Some grasslands may well have open access features, for example; but then that's true of many forests, as well.
Here is a project about payment for ES in Portugal. The partners are Coca-Cola and WWF and with the support of CEABN research center. The objective is to compensate landowners for the ecosystem services they provide.
The RISEMP project (2002 - 2008) targeted silvopastoral practices in 3 Latin American countries. Maybe you can find something useful in the information of the project (https://www.thegef.org/gef/node/2224).