We consider exclusive pp → ppπ+π − and pp → ppπ+π −π +π − reactions at high energies. The calculation is based on a tensor pomeron model and the amplitudes for the processes are formulated in an effective field-theoretic approach. In the case of pp → ppπ+π − process we consider both diffractive and photoproduction mechanisms and we include the non-resonant π +π − continuum and the resonance f0(500), f0(980), f2(1270), ρ(770) contributions. We discuss how two pomerons couple to tensor meson f2(1270) and the interference effects of resonance and dipion continuum. We find that the relative contribution of resonances ρ(770), f2(1270) and dipion continuum strongly depends on the cut on proton transverse momenta. In the case of exclusive central 4π production we include the contribution via the intermediate σσ and ρρ states. For both processes the theoretical results have been compared with the experimental data and predictions for planned or being carried out experiments (e.g. STAR, ATLAS-ALFA) are presented.