High-performance reconfigurable computers (HPRCs) consisting of CPUs with application-specific FPGA accelerators traditionally use a low-level hardware-description language such as VHDL or Verilog to program the FP-GAs. The complexity of hardware design methodologies for FPGAs requires specialist engineering knowledge and presents a significant barrier to entry for scientific users with only a software background. Recently, a number of High-Level Languages (HLLs) for programming FPGAs have emerged that aim to lower this barrier and abstract away hardware-dependent details. This paper presents the results of a study on implementing hardware accelerators using the Mitrion-C HLL. The implementation of two floating-point scientific kernels: dense matrix-vector multiplication (DMVM) and the computation of spherical boundary conditions in molecular dynamics (SB) are described. We describe optimizations that are essential for taking advantage of both the features of the HLL and the underlying HPRC hardware and libraries. Scaling of the algorithms to multiple FPGAs is also investigated. With four FPGAs, 80 times speedup over an Itanium 2 CPU was achieved for the DMVM, while a 26 times speedup was achieved for SB.