The aim of this paper is to show that the corona \(P_n \bigodot P_m\) between two paths \(P_n\) and \(P_m\) is cordial for all \(n \geq 1\) and \(m \geq 1\). Also, we prove that except for \(n\) and \(m\) being congruent to \(2 \pmod{4}\), the corona \(C_n \bigodot C_m\) between two cycles \(C_n\) and \(C_m\) is cordial. Furthermore, we show that if \(n \equiv 2 \pmod{4}\) and \(m\) is odd, then \(C_n \bigodot C_m\) is not cordial.