jqGrid support search toolbar mode, where you can have search toolbar on top of each column of the grid. To use, call the filterToolbar method. You can exclude certain columns from appearing in the search options by setting the search property of the respective column to false.
As of version 4.5 we support operations on toolbar search fields. To do this it is needed to set "searchOperators" to true in Filter Options.
With the sopt property of each column we can set different operations
When searching is performed the grid triggers Searching / Searched event which you can use to customize this behavior.