Core–shell-type polymers based on a hyperbranched (hb) poly(ethylenimine) core and a shell with a variable maltose content were applied as coating materials for fused silica capillaries. A new, simple, fast, and reproducible way of modifying the capillary walls through the physical adsorption of the core–shell-type polymers using a Cu²⁺ support was developed. The coating created by this method was found to be very stable compared to the coating created using a solution of the polymer only. Capillaries modified with the core–shell-type polymers were tested by applying them to the electrophoretic separation of catecholamines and proteins. The modified capillaries showed high efficiencies (up to 800,000 theoretical plates per meter for lysozyme) and separation selectivities. The highest efficiency was achieved using capillaries modified with the polymer containing the lowest content of maltose in the shell and the most accessible positively charged core. Various online concentration techniques were also tested as a means to lower detection limits further, making it possible to analyze proteins in biological fluids (saliva) as well as catecholamines in human urine after SPE using activated alumina.