Let D_n denote the set of monotone Boolean functions with n variables. The cardinality of D_n, denoted by d_n, is known as the n-th Dedekind number. Elements of D_n can be represented as strings of bits of length 2ⁿ. For each f ∈ D_n, we have the dual function f^* ∈ D_n which is obtained by reversing and negating all bits. An element f ∈ D_n is self-dual if f = f^*. Let Λ_n denote the set of all self-dual monotone Boolean functions of n variables and let λ_n denote |Λ_n|. There is a natural action of the permutation group S_n on the set of Boolean functions by permutation of variables. The sets D_n and Λ_n are closed under this action. We let R_n and Q_n denote the sets of all equivalence classes in D_n and Λ_n, respectively. In this paper, we derive several algorithms for counting self-dual monotone Boolean functions and confirm the known result that λ₉ equals 423,295,099,074,735,261,880. Furthermore, we calculate |Q₈| to be 6,001,501.