Karimi lost to Azerbaijan’s Turan Bayramov 6-1 in the final match of the 65kg weight category.
The bronze medal went to Inayat Ullah from Pakistan.
In the final match of the 110kg, Zare was defeated against Russian Sergei Kozyrev 6-5 and claimed a silver.
Egyptian Ahmed Mahmoud Khalil won the bronze medal.
Iranian Greco-Roman wrestlers Amir Reza Dehbozorgi (45kg) and Mohammad Nosrati (92kg) had already won two gold medals in the Games.
Wrestling at the 2018 Summer Youth Olympics was held from October 12 to 14.
The event took place at the Parque Polideportivo Roca in Buenos Aires, Argentina.