How good were climate models of the 1990s at predicting the global temperature trends of the 2000s/2010s?
You might take a look at the Technical Summary of the most recent IPCC Assessment Report (5).
Thematic Focus Element #3 is &quot;Comparing Projections from Previous IPCC Assessments with Observations&quot;
It says:

Global Mean Temperature Anomaly
Relative to the 1961–1990 mean, the GMST anomaly has been positive and
larger than 0.25°C since 2001. Observations are generally well within
the range of the extent of the earlier IPCC projections (TFE.3,
Figure1, middle left) This is also true for the Coupled Model
Intercomparison Project Phase 5 (CMIP5) results (TFE.3, Figure 1;
middle right) in the sense that the observed record lies within the
range of the model projections, but on the lower end of the plume. Mt
Pinatubo erupted in 1991 (see FAQ 11.2 for discussion of how volcanoes
impact the climate system), leading to a brief period of relative
global mean cooling during the early 1990s. The IPCC First, Second and
Third Assessment Reports (FAR, SAR and TAR) did not include the
effects of volcanic eruptions and thus failed to include the cooling
associated with the Pinatubo eruption. AR4 and AR5, however, did
include the effects from volcanoes and did simulate successfully the
associated cooling. During 1995–2000 the global mean temperature
anomaly was quite variable—a significant fraction of this variability
was due to the large El Niño in 1997–1998 and the strong back-to-back
La Niñas in 1999–2001. The projections associated with these
assessment reports do not attempt to capture the actual evolution of
these El Niño and La Niña events, but include them as a source of
uncertainty due to natural variability as encompassed by, for example,
the range given by the individual CMIP3 and CMIP5 simulations and
projection (TFE.3, Figure 1). The grey wedge in TFE.3, Figure 1
(middle right) corresponds to the indicative likely range for annual
temperatures, which is determined from the Representative
Concentration Pathways (RCPs) assessed value for the 20-year mean
2016–2035 (see discussion of Figure TS.14 and Section 11.3.6 for
details). From 1998 to 2012 the observational estimates have largely
been on the low end of the range given by the scenarios alone in
previous assessment reports and CMIP3 and CMIP5 projections. {2.4; Box
9.2}

I've attached an image as well from that summary:


Estimated changes in the
observed globally and annually averaged surface temperature anomaly
relative to 1961–1990 (in °C) since 1950 compared with the range of
projections from the previous IPCC assessments. Values are harmonized
to start from the same value at 1990. Observed global annual
temperature anomaly, relative to 1961–1990, from three data sets is
shown as squares and smoothed time series as solid lines from the
Hadley Centre/Climatic Research Unit gridded surface temperature data
set 4 (HadCRUT4; bright green), Merged Land–Ocean Surface Temperature
Analysis (MLOST; warm mustard) and Goddard Institute for Space Studies
Surface Temperature Analysis (GISTEMP; dark blue) data sets. The
coloured shading shows the projected range of global annual mean near
surface temperature change from 1990 to 2035 for models used in FAR
(Figure 6.11), SAR (Figure 19 in the TS of IPCC 1996), TAR (full range
of TAR, Figure 9.13(b)). TAR results are based on the simple climate
model analyses presented in this assessment and not on the individual
full three-dimensional climate model simulations. For the AR4 results
are presented as single model runs of the CMIP3 ensemble for the
historical period from 1950 to 2000 (light grey lines) and for three
SRES scenarios (A2, A1B and B1) from 2001 to 2035. For the three SRES
scenarios the bars show the CMIP3 ensemble mean and the likely range
given by –40 % to +60% of the mean as assessed in Chapter 10 of AR4.