A subset \( X \) of the vertex set of a graph \( G \) is a secure dominating set of \( G \) if \( X \) is a dominating set of \( G \) and if, for each vertex \( u \) not in \( X \), there is a neighboring vertex \( v \) of \( u \) in \( X \) such that the swap set \( (X – \{v\}) \cup \{u\} \) is again a dominating set of \( G \). The secure domination number of \( G \), denoted by \( \gamma_s(G) \), is the cardinality of a smallest secure dominating set of \( G \). In this paper, we present two algorithms (a branch-and-reduce algorithm as well as a branch-and-bound algorithm) for determining the secure domination number of a general graph \( G \) of order \( n \). The worst-case time complexities of both algorithms are \( \mathcal{O}(2^{n-s-\sum_{i=1}^{k}(|\mathcal{R}_i|-1)}) \), where \( s \) is the number of support vertices in \( G \) and \( \mathcal{R}_i, \ldots, \mathcal{R}_k \) are the redundancy classes of \( G \) (two vertices are in the same redundancy class if they are adjacent and share the same closed neighborhood which forms a clique in \( G \)).