  We study the prospects of finding the first quasars in the universe with ALMA
and JWST. For this purpose, we derive a model for the high-redshift black hole
population based on observed relations between the black hole mass and the host
galaxy. We re-address previous constraints from the X-ray background with
particular focus on black hole luminosities below the Eddington limit as
observed in many local AGN. For such luminosities, up to 20% of high-redshift
black holes can be active quasars. We then discuss the observables of
high-redshift black holes for ALMA and JWST by adopting NGC 1068 as a reference
system. We calculate the expected flux of different fine-structure lines for a
similar system at higher redshift, and provide further predictions for high-J
CO lines. We discuss the expected fluxes from stellar light, the AGN continuum
and the Lyman $\alpha$ line for JWST. Line fluxes observed with ALMA can be
used to derive detailed properties of high-redshift sources. We suggest two
observational strategies to find potential AGN at high redshift and estimate
the expected number of sources, which is between 1-10 for ALMA with a field of
view of $\sim(1')^2$ searching for line emission and 100-1000 for JWST with a
field of view of $(2.16')^2$ searching for continuum radiation. We find that
both telescopes can probe high-redshift quasars down to redshift 10 and beyond,
and therefore truely detect the first quasars in the universe.
