The application of the Very Long Baseline Interferometry (VLBI) technique for observations of artificial Earth-orbiting satellites instead of extra-galactic radio sources has been vividly discussed in the geodetic community for several years. Promising applications - among others - can be found in the field of inter-technique frame ties. In this respect, the fundamental idea is to establish a co-location in space by combining the sensors of different space-geodetic techniques on a common satellite platform orbiting the Earth. Observations of this satellite can then be used to connect the technique-specific coordinate frame solutions. This approach is particularly relevant for the realization of the International Terrestrial Reference Frame (ITRF), which is a combination product of long-term time series of observations with VLBI, Satellite Laser Ranging (SLR), Global Navigation Satellite Systems (GNSS), and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS). Additionally, the ITRF combination fundamentally relies on so-called local ties -- terrestrially measured vectors between the reference points of geodetic instruments at co-location sites. Connecting the individual techniques via a co-location in space (i.e. by establishing so-called space ties), complementary to using local ties, provides promising possibilities to reveal technique-specific biases, and to investigate discrepancies between local tie vectors and space geodetic coordinate solutions which are widely present on the cm level. Additionally, a co-location in space promotes the rigorous integration of all space-geodetic techniques, which was identified as one of the main goals of the Global Geodetic Observing System (GGOS) of the International Association of Geodesy (IAG). From the perspective of VLBI, satellite observations would allow to connect the purely geometric coordinate frame realized by VLBI observations of extremely remote radio sources, with the dynamic coordinate frames of the geodetic satellite techniques (GNSS, SLR, and DORIS) which are subject to the Earth's gravity field. Although space ties between the satellite techniques have already been shown, the space tie with VLBI has not been realized so far, and could only be studied by simulations. One of the main reasons for this deficiency is, that actual observation data is widely missing. Observations of satellites with geodetic VLBI systems are non-standard, and the required observation and analysis processes were not in place in order to collect real observation data. Encountering this issue, a goal of this work was to establish -- for the first time -- a closed process chain which enables to obtain group delays based on observations of satellites with VLBI. This process chain includes all required processes from scheduling, over observations, correlation and post-correlation processing, to the final analysis of the delays. To stay as close as possible to data acquisition and processing scheme which is operationally used for geodetic VLBI sessions, standard software tools were adopted for satellite observations: The Vienna VLBI and Satellite Software (VieVS) was used for scheduling and data analysis, the software DiFX for correlation, and the Haystack Observatory Postprocessing System (HOPS) for the fringe fitting. The second goal of this work was to apply the established process chain to perform actual observation experiments, in order to validate and test all processing steps, and to refine and adapt them whenever necessary. Hence, in 2015 and 2016 a series of VLBI sessions with observations of GNSS satellites (GPS and GLONASS) was carried out mainly on the Australian baseline Hobart-Ceduna. End of 2016 the network was extended by the antenna at Warkworth (New Zealand). All antennas were equipped with L-band receivers suitable to record the GNSS L1 and L2 signals, and with modern backends. The final experiments in this series lasted for up to 6 h and yielded results in terms of observed minus computed (O-C) residuals on the level of a few ns. In November 2016 the Chinese APOD-A nano satellite was tracked over a few days whenever visible by the Australian AuScope VLBI array. This small cube satellite was a particularly interesting observation target, as it can be considered as a first realization of a co-location satellite enabling GNSS, SLR, and VLBI on a common platform in a low Earth orbit (LEO). APOD was equipped with a dedicated VLBI beacon emitting narrow-bandwidth tones in the S- and X-band that could be observed with standard receiver equipment used for geodetic application. Although APOD was challenging to track due to the low orbit height of about 450 km, all observations were successfully correlated, and yielded O-C residuals below 10 ns. All experiments are described in detail within this thesis. Although the results of the conducted satellite observation experiments did not reach an accuracy level which would allow for studying actual frame ties with VLBI, the work is still valuable due to the gained hands-on observation experience. Furthermore, the newly developed procedures and programs now enable to perform more observations in a semi-manual manner, similar to standard observations of natural radio sources -- enabling further research and development in the field of VLBI satellite observations.