Boron substitution represents a promising approach to stabilize carbon clathrate structures, but no thermodynamically stable substitution schemes have been identified for frameworks other than the type-VII (sodalite) structure type. To investigate the possibility for additional tetrahedral carbon-based clathrate networks, more than 5000 unique boron decoration schemes were investigated computationally for type-I and type-II carbon clathrates with a range of guest elements including Li, Na, K, Rb, Cs, Mg, Ca, Sr, and Ba. Density functional theory calculations were performed at 10 and 50 GPa, and the stability and impact of boron substitution were evaluated. The results indicate that the boron-substituted carbon clathrates are stabilized under high-pressure conditions. Full cage occupancies of intermediate-sized guest atoms (e.g., Na, Ca, and Sr) are the most favorable energetically. Clathrate stability is maximized when the boron atoms are substituted within the hexagonal rings of the large [51262]/[51264] cages. Several structures with favorable formation enthalpies <-200 meV/atom were predicted, and type-I Ca8B16C30 is on the convex hull at 50 GPa. This structure represents the first thermodynamically stable type-I clathrate identified and suggests that boron-substituted carbon clathrates may represent a large family of diamond-like framework materials with a range of structure types and guest/framework substitutions.