Higher-order constructs extend the expressiveness of first-order (Constraint) Logic Programming ((C)LP) both syntactically and semantically. At the same time assertions have been in use for some time in (C)LP systems helping programmers detect errors and validate programs. However, these assertion-based extensions to (C)LP have not been integrated well with higher-order to date. This paper contributes to filling this gap by extending the assertion-based approach to error detection and program validation to the higher-order context within (C)LP. We propose an extension of properties and assertions as used in (C)LP in order to be able to fully describe arguments that are predicates. The extension makes the full power of the assertion language available when describing higher-order arguments. We provide syntax and semantics for (higher-order) properties and assertions, as well as for programs which contain such assertions, including the notions of error and partial correctness. We also discuss several alternatives for performing run-time checking of such programs.