Systems including light-emitting diodes (LEDs) are provided. The systems include one or more wavelength-converting member(s) that is/are remote from the emission surface of one or more LED-based light source(s). The wavelength-converting member may be separated from the emission surface of a first LED and positioned such that light emitted from the first LED is absorbed by the wavelength-converting material. The wavelength-converting material emits secondary light having a different wavelength than the wavelength of the light emitted from the first LED. The systems may include a second light source comprising a second LED configured to emit light having a wavelength from an emission surface and a wavelength-combining element configured to combine the secondary light from the wavelength-converting member and the light emitted from the second light source to form a co-axial light beam.