Today's distributed programs are often written using either explicit message passing or Remote Procedure Calls (RPCs) that are not natively integrated in the language. It is difficult to establish the correctness of programs written this way compared to programs written for a single computer. We propose a generalisation of RPCs that are natively integrated in a functional programming language meaning that they have support for higher-order calls across node boundaries. Our focus is on how such languages can be compiled correctly and efficiently. We present four different solutions. Two of them are based on interaction semantics --- the Geometry of Interaction and game semantics --- and two are extensions of conventional abstract machines --- the Krivine machine and the SECD machine. To target as general distributed systems as possible our solutions support RPCs without sending code. We prove the correctness of the abstract machines with respect to their single-node execution, and show their viability for use for compilation by implementing prototype compilers based on them. The conventionally based machines are shown to enable efficient programs. Our intention is that these abstract machines can form the foundation for future programming languages that use the idea of higher-order RPCs.